Professor Aazami’s research area is in differential geometry; in particular, in Lorentzian and Riemannian geometry. He also studies gravitational lensing, which is the bending of light by gravity.<\/p>\n
He has taught a variety of courses at Clark, from Honors Calculus to Measure Theory, as well as created two new courses on Quantitative Finance and the Mathematics of Voting and Social Choice. He has also self-published a textbook titled “48 Hours of Honors Calculus.”<\/p>\n","protected":false},"author":0,"featured_media":1821,"parent":0,"template":"","meta":{"cu_faculty_f180_userid":"C70244964","cu_faculty_first_name":"Amir Babak","cu_faculty_last_name":"Aazami","cu_faculty_employment_status":"Full Time","cu_faculty_rank":"Associate Professor","cu_faculty_position":"Associate Professor","cu_faculty_phone":"","cu_faculty_email":"AAazami@clarku.edu","cu_faculty_location":"","cu_faculty_about":"
Professor Aazami's research area is in differential geometry; in particular, in Lorentzian and Riemannian geometry. He also studies gravitational lensing, which is the bending of light by gravity.<\/p>\n
He has taught a variety of courses at Clark, from Honors Calculus to Measure Theory, as well as created two new courses on Quantitative Finance and the Mathematics of Voting and Social Choice. He has also self-published a textbook titled \"48 Hours of Honors Calculus.\"<\/p>","cu_faculty_degrees":"Ph.D. in Mathematics,<\/span> Duke University, 2011","cu_faculty_cv":"https:\/\/faculty180.interfolio.com\/public\/download.php?key=SDRwNCtxSUpsamxBQ213WS9ucHFuNnMwT0hzQU11b2RPQkJ2cWc3amxyUmNRdVVXTkF4MU1zT21qREtJZEdWZ1Z0cnphRERiRUYzM3JJdXhzTEZCdDBFTDZCV2t4R2FITzRISForVUQwcnc9","cu_faculty_links":"[]","cu_faculty_scholarly_interests":"","cu_faculty_scholarly_works":"[{\"activityid\":13402,\"fields\":{\"Type\":\"Articles in Refereed Journals\",\"Title\":\"<p>Petrov Types for the Weyl Tensor via the Riemannian-to-Lorentzian Bridge<\\\/p>\",\"Journal Title\":\"\",\"Series Title\":\"\",\"Month \\\/ Season\":\"\",\"Year\":2025,\"Publisher\":\"\",\"Publisher City and State\":\"\",\"Publisher Country\":\"\",\"Volume\":\"\",\"Issue Number \\\/ Edition\":\"\",\"Page Number(s) or Number of Pages\":\"\",\"ISSN\":\"\",\"DOI\":\"\",\"CoAuthor\":null,\"URL\":\"http:\\\/\\\/arxiv.org\\\/abs\\\/2412.20915v1\",\"Description\":\"<p>We analyze oriented Riemannian 4-manifolds whose Weyl tensors $W$ satisfy the conformally invariant condition $W(T,\\\\cdot,\\\\cdot,T) = 0$ for some nonzero vector $T$. While this can be algebraically classified via $W$'s normal form, we find a further geometric classification by deforming the metric into a Lorentzian one via $T$. We show that such a $W$ will have the analogue of Petrov Types from general relativity, that only Types I and D can occur, and that each is completely determined by the number of critical points of $W$'s associated Lorentzian quadratic form. A similar result holds for the Lorentzian version of this question, with $T$ timelike.<\\\/p>\",\"Include description in output citation\":0,\"Origin\":\"arXiv\"},\"facultyid\":\"C70244964\",\"status\":[{\"id\":13402,\"status\":\"Submitted\",\"term\":\"Spring\",\"year\":2025,\"termid\":\"2024\\\/03\",\"listingorder\":2,\"completionorder\":2},{\"id\":13402,\"status\":\"Submitted\",\"term\":\"Summer\",\"year\":2024,\"termid\":\"2023\\\/05\",\"listingorder\":2,\"completionorder\":2}],\"userid\":\"C70244964\",\"attachments\":[],\"coauthors_list\":[\"Amir B Aazami\"],\"sort_date\":\"2025-01-01\"},{\"activityid\":13404,\"fields\":{\"Type\":\"Articles in Refereed Journals\",\"Title\":\"<p>On the Curvature and Topology of Compact Stationary Spacetimes<\\\/p>\",\"Journal Title\":\"\",\"Series Title\":\"\",\"Month \\\/ Season\":\"\",\"Year\":2025,\"Publisher\":\"\",\"Publisher City and State\":\"\",\"Publisher Country\":\"\",\"Volume\":\"\",\"Issue Number \\\/ Edition\":\"\",\"Page Number(s) or Number of Pages\":\"\",\"ISSN\":\"\",\"DOI\":\"\",\"CoAuthor\":null,\"URL\":\"http:\\\/\\\/arxiv.org\\\/abs\\\/2502.00541v1\",\"Description\":\"<p>Using the result of Petersen $\\\\&$ Wink '21, we find obstructions to the curvature and topology of compact Lorentzian manifolds admitting a unit-length timelike Killing vector field.<\\\/p>\",\"Include description in output citation\":0,\"Origin\":\"arXiv\"},\"facultyid\":\"C70244964\",\"status\":[{\"id\":13404,\"status\":\"Submitted\",\"term\":\"Spring\",\"year\":2025,\"termid\":\"2024\\\/03\",\"listingorder\":2,\"completionorder\":2},{\"id\":13404,\"status\":\"Submitted\",\"term\":\"Summer\",\"year\":2024,\"termid\":\"2023\\\/05\",\"listingorder\":2,\"completionorder\":2}],\"userid\":\"C70244964\",\"attachments\":[],\"coauthors_list\":[\"Amir B Aazami\"],\"sort_date\":\"2025-01-01\"},{\"activityid\":13406,\"fields\":{\"Type\":\"Presentations\",\"Title of Presentation\":\"<p>"Democracy and Game Theory"<\\\/p>\",\"Conference \\\/ Meeting Name\":\"\",\"Location of Conference \\\/ Meeting\":\"Duke University\",\"Month \\\/ Season\":\"\",\"Year\":2024,\"Sponsoring Organization\":\"\",\"CoAuthor\":null,\"URL\":\"\",\"Description\":\"\",\"Include description in output citation\":0,\"Origin\":\"Manual\"},\"facultyid\":\"C70244964\",\"status\":[{\"id\":13406,\"status\":\"Completed\\\/Published\",\"term\":\"Fall\",\"year\":2024,\"termid\":\"2024\\\/01\",\"listingorder\":6,\"completionorder\":6}],\"userid\":\"C70244964\",\"attachments\":[],\"coauthors_list\":[\"Amir Babak Aazami\"],\"sort_date\":\"2024-9-01\"},{\"activityid\":13408,\"fields\":{\"Type\":\"Presentations\",\"Title of Presentation\":\"<p>"Films, Finance, and Wildfires \\u2013 how geometry\\u00a0gets used in the real world"<\\\/p>\",\"Conference \\\/ Meeting Name\":\"\",\"Location of Conference \\\/ Meeting\":\"Union College\",\"Month \\\/ Season\":\"\",\"Year\":2024,\"Sponsoring Organization\":\"\",\"CoAuthor\":null,\"URL\":\"\",\"Description\":\"\",\"Include description in output citation\":0,\"Origin\":\"Manual\"},\"facultyid\":\"C70244964\",\"status\":[{\"id\":13408,\"status\":\"Completed\\\/Published\",\"term\":\"Fall\",\"year\":2024,\"termid\":\"2024\\\/01\",\"listingorder\":6,\"completionorder\":6}],\"userid\":\"C70244964\",\"attachments\":[],\"coauthors_list\":[\"Amir Babak Aazami\"],\"sort_date\":\"2024-9-01\"},{\"activityid\":11321,\"fields\":{\"Type\":\"Presentations\",\"Title of Presentation\":\""Almost-Einstein" metrics, normal forms, and Petrov Types on 4-manifolds\",\"Conference \\\/ Meeting Name\":\"\",\"Location of Conference \\\/ Meeting\":\"Technical University of Denmark\",\"Month \\\/ Season\":\"March\",\"Year\":2024,\"Sponsoring Organization\":\"\",\"CoAuthor\":null,\"URL\":\"\",\"Description\":\"\",\"Include description in output citation\":0,\"Origin\":\"Manual\"},\"facultyid\":\"C70244964\",\"status\":[{\"id\":11321,\"status\":\"Completed\\\/Published\",\"term\":\"Spring\",\"year\":2024,\"termid\":\"2023\\\/03\",\"listingorder\":6,\"completionorder\":6}],\"userid\":\"C70244964\",\"attachments\":[],\"coauthors_list\":[\"Amir Babak Aazami\"],\"sort_date\":\"2024-3-01\"},{\"activityid\":13397,\"fields\":{\"Type\":\"Articles in Refereed Journals\",\"Title\":\"<p>Geometry via Plane wave limits<\\\/p>\",\"Journal Title\":\"\",\"Series Title\":\"\",\"Month \\\/ Season\":\"\",\"Year\":2024,\"Publisher\":\"\",\"Publisher City and State\":\"\",\"Publisher Country\":\"\",\"Volume\":\"\",\"Issue Number \\\/ Edition\":\"\",\"Page Number(s) or Number of Pages\":\"\",\"ISSN\":\"\",\"DOI\":\"\",\"CoAuthor\":null,\"URL\":\"http:\\\/\\\/arxiv.org\\\/abs\\\/2408.02567v3\",\"Description\":\"<p>Utilizing the covariant formulation of Penrose's plane wave limit by Blau et~al., we construct for any semi-Riemannian metric $g$ a family of "plane wave limits." These limits are taken along any geodesic of $g$, yield simpler metrics of Lorentzian signature, and are isometric invariants. We show that they generalize Penrose's limit to the semi-Riemannian regime and, in certain cases, encode $g$'s tensorial geometry and its geodesic deviation. As an application of the latter, we partially extend a well known result by Hawking & Penrose to the semi-Riemannian regime: On any semi-Riemannian manifold, if the Ricci curvature is nonnegative along any complete geodesic without conjugate points that is "causally independent" (in a sense we make precise), then the curvature tensor along that geodesic must vanish in all normal directions. A Morse Index Theorem is also proved for such geodesics.<\\\/p>\",\"Include description in output citation\":0,\"Origin\":\"arXiv\"},\"facultyid\":\"C70244964\",\"status\":[{\"id\":13397,\"status\":\"Submitted\",\"term\":\"Fall\",\"year\":2024,\"termid\":\"2024\\\/01\",\"listingorder\":2,\"completionorder\":2},{\"id\":13397,\"status\":\"Submitted\",\"term\":\"Summer\",\"year\":2024,\"termid\":\"2023\\\/05\",\"listingorder\":2,\"completionorder\":2}],\"userid\":\"C70244964\",\"attachments\":[],\"coauthors_list\":[\"Amir B Aazami\"],\"sort_date\":\"2024-01-01\"},{\"activityid\":13398,\"fields\":{\"Type\":\"Articles in Refereed Journals\",\"Title\":\"<p>The Eisenhart Lift and Hamiltonian Systems<\\\/p>\",\"Journal Title\":\"\",\"Series Title\":\"\",\"Month \\\/ Season\":\"\",\"Year\":2024,\"Publisher\":\"\",\"Publisher City and State\":\"\",\"Publisher Country\":\"\",\"Volume\":\"\",\"Issue Number \\\/ Edition\":\"\",\"Page Number(s) or Number of Pages\":\"\",\"ISSN\":\"\",\"DOI\":\"\",\"CoAuthor\":null,\"URL\":\"http:\\\/\\\/arxiv.org\\\/abs\\\/2408.16139v1\",\"Description\":\"<p>It is well known in general relativity that trajectories of Hamiltonian systems lift to geodesics of pp-wave spacetimes, an example of a more general phenomenon known as the "Eisenhart lift." We review and expand upon the benefits of this correspondence for dynamical systems theory. One benefit is the use of curvature and conjugate points to study the stability of Hamiltonian systems. Another benefit is that this lift unfolds a Hamiltonian system into a family of ODEs akin to a moduli space. One such family arises from the conformal invariance of lightlike geodesics, by which any Hamiltonian system unfolds into a "conformal class" of non-diffeomorphic ODEs with solutions in common. By utilizing higher-index versions of pp-waves, a similar lift and conformal class are shown to exist for certain second-order complex ODEs. Another such family occurs by lifting to a Riemannian metric that is dual to a pp-wave, a process that in certain cases yields a "square root" for the Hamiltonian. We prove a two-point boundary result for the family of ODEs arising from this lift, as well as the existence of a constant of the motion generalizing conservation of energy.<\\\/p>\",\"Include description in output citation\":0,\"Origin\":\"arXiv\"},\"facultyid\":\"C70244964\",\"status\":[{\"id\":13398,\"status\":\"Submitted\",\"term\":\"Fall\",\"year\":2024,\"termid\":\"2024\\\/01\",\"listingorder\":2,\"completionorder\":2},{\"id\":13398,\"status\":\"Submitted\",\"term\":\"Summer\",\"year\":2024,\"termid\":\"2023\\\/05\",\"listingorder\":2,\"completionorder\":2}],\"userid\":\"C70244964\",\"attachments\":[],\"coauthors_list\":[\"Amir B Aazami\"],\"sort_date\":\"2024-01-01\"},{\"activityid\":7168,\"fields\":{\"Type\":\"Articles in Refereed Journals\",\"Title\":\"<p>Obstructions to distinguished Riemannian metrics via Lorentzian geometry<\\\/p>\",\"Journal Title\":\"Advances in Theoretical and Mathematical Physics\",\"Series Title\":\"\",\"Month \\\/ Season\":\"\",\"Year\":2023,\"Publisher\":\"\",\"Publisher City and State\":\"\",\"Publisher Country\":\"\",\"Volume\":\"\",\"Issue Number \\\/ Edition\":\"\",\"Page Number(s) or Number of Pages\":\"\",\"ISSN\":\"\",\"DOI\":\"\",\"CoAuthor\":null,\"URL\":\"http:\\\/\\\/arxiv.org\\\/abs\\\/2207.14701v1\",\"Description\":\"\",\"Include description in output citation\":0,\"Origin\":\"arXiv\"},\"facultyid\":\"C70244964\",\"status\":[{\"id\":7168,\"status\":\"Completed\\\/Published\",\"term\":\"Fall\",\"year\":2023,\"termid\":\"2023\\\/01\",\"listingorder\":6,\"completionorder\":6}],\"userid\":\"C70244964\",\"attachments\":[],\"coauthors_list\":[\"Amir Babak Aazami\"],\"sort_date\":\"2023-9-01\"},{\"activityid\":11322,\"fields\":{\"Type\":\"Presentations\",\"Title of Presentation\":\"Gravitational waves in vacuum? \\u00a0On the Ehlers-Kundt conjecture\",\"Conference \\\/ Meeting Name\":\"\",\"Location of Conference \\\/ Meeting\":\"Duke Kunshan University, Kunshan, China\",\"Month \\\/ Season\":\"September\",\"Year\":2023,\"Sponsoring Organization\":\"\",\"CoAuthor\":null,\"URL\":\"\",\"Description\":\"\",\"Include description in output citation\":0,\"Origin\":\"Manual\"},\"facultyid\":\"C70244964\",\"status\":[{\"id\":11322,\"status\":\"Completed\\\/Published\",\"term\":\"Fall\",\"year\":2023,\"termid\":\"2023\\\/01\",\"listingorder\":6,\"completionorder\":6}],\"userid\":\"C70244964\",\"attachments\":[],\"coauthors_list\":[\"Amir Babak Aazami\"],\"sort_date\":\"2023-9-01\"},{\"activityid\":4236,\"fields\":{\"Type\":\"Articles in Refereed Journals\",\"Title\":\"Killing vector fields on Riemannian and Lorentzian 3-manifolds\",\"Journal Title\":\"Mathematische Nachrichten\",\"Series Title\":\"\",\"Month \\\/ Season\":\"\",\"Year\":2023,\"Publisher\":\"\",\"Publisher City and State\":\"\",\"Publisher Country\":\"\",\"Volume\":\"\",\"Issue Number \\\/ Edition\":\"\",\"Page Number(s) or Number of Pages\":\"\",\"ISSN\":\"\",\"DOI\":\"\",\"CoAuthor\":null,\"URL\":\"http:\\\/\\\/arxiv.org\\\/abs\\\/2011.01144v1\",\"Description\":\"\",\"Include description in output citation\":0,\"Origin\":\"Manual\"},\"facultyid\":\"C70244964\",\"status\":[{\"id\":4236,\"status\":\"Completed\\\/Published\",\"term\":\"Spring\",\"year\":2023,\"termid\":\"2022\\\/03\",\"listingorder\":6,\"completionorder\":6}],\"userid\":\"C70244964\",\"attachments\":[],\"coauthors_list\":[\"Robert O. Ream\",\"Amir B. Aazami\"],\"sort_date\":\"2023-1-01\"},{\"activityid\":5991,\"fields\":{\"Type\":\"Articles in Refereed Journals\",\"Title\":\"Finsler pp-waves and the Penrose Limit\",\"Journal Title\":\"General Relativity and Gravitation\",\"Series Title\":\"\",\"Month \\\/ Season\":\"\",\"Year\":2023,\"Publisher\":\"\",\"Publisher City and State\":\"\",\"Publisher Country\":\"\",\"Volume\":\"\",\"Issue Number \\\/ Edition\":\"\",\"Page Number(s) or Number of Pages\":\"\",\"ISSN\":\"\",\"DOI\":\"\",\"CoAuthor\":null,\"URL\":\"http:\\\/\\\/arxiv.org\\\/abs\\\/2205.01162v1\",\"Description\":\"\",\"Include description in output citation\":0,\"Origin\":\"arXiv\"},\"facultyid\":\"C70244964\",\"status\":[{\"id\":5991,\"status\":\"Completed\\\/Published\",\"term\":\"Spring\",\"year\":2023,\"termid\":\"2022\\\/03\",\"listingorder\":6,\"completionorder\":6}],\"userid\":\"C70244964\",\"attachments\":[],\"coauthors_list\":[\"Amir Babak Aazami\"],\"sort_date\":\"2023-1-01\"},{\"activityid\":5993,\"fields\":{\"Type\":\"Articles in Refereed Journals\",\"Title\":\"Exact Parallel Waves in General Relativity\",\"Journal Title\":\"General Relativity and Gravitation (Special Issue on \\u201cSingularity Theorems, causality, and all that (SCRI21),\\u201d in honor of Roger Penrose)\",\"Series Title\":\"\",\"Month \\\/ Season\":\"\",\"Year\":2023,\"Publisher\":\"\",\"Publisher City and State\":\"\",\"Publisher Country\":\"\",\"Volume\":\"\",\"Issue Number \\\/ Edition\":\"\",\"Page Number(s) or Number of Pages\":\"\",\"ISSN\":\"\",\"DOI\":\"\",\"CoAuthor\":null,\"URL\":\"\",\"Description\":\"\",\"Include description in output citation\":0,\"Origin\":\"Manual\"},\"facultyid\":\"C70244964\",\"status\":[{\"id\":5993,\"status\":\"Completed\\\/Published\",\"term\":\"Spring\",\"year\":2023,\"termid\":\"2022\\\/03\",\"listingorder\":6,\"completionorder\":6}],\"userid\":\"C70244964\",\"attachments\":[],\"coauthors_list\":[\"Amir Babak Aazami\",\"Cian Roche\",\"Carla Cederbaum\"],\"sort_date\":\"2023-1-01\"},{\"activityid\":13396,\"fields\":{\"Type\":\"Articles in Refereed Journals\",\"Title\":\"<p>On the Petrov Type of a 4-manifold<\\\/p>\",\"Journal Title\":\"\",\"Series Title\":\"\",\"Month \\\/ Season\":\"\",\"Year\":2023,\"Publisher\":\"\",\"Publisher City and State\":\"\",\"Publisher Country\":\"\",\"Volume\":\"\",\"Issue Number \\\/ Edition\":\"\",\"Page Number(s) or Number of Pages\":\"\",\"ISSN\":\"\",\"DOI\":\"\",\"CoAuthor\":null,\"URL\":\"http:\\\/\\\/arxiv.org\\\/abs\\\/2309.13717v2\",\"Description\":\"<p>On an oriented 4-manifold, we examine the geometry that arises when the curvature operator of a Riemannian or Lorentzian metric $g$ commutes, not with its own Hodge star operator, but rather with that of another semi-Riemannian metric $h$ that is a suitable deformation of $g$. We classify the case when one of these metrics is Riemannian and the other Lorentzian by generalizing the concept of Petrov Type from general relativity; the case when $h$ is split-signature is also examined. The "generalized Petrov Types" so obtained are shown to relate to the critical points of $g$'s sectional curvature, and sometimes yield unique normal forms. They also carry topological information independent of the Hitchin-Thorpe inequality, and yield a direct geometric formulation of "almost-Einsten" metric via the Ricci or sectional curvature of $g$.<\\\/p>\",\"Include description in output citation\":0,\"Origin\":\"arXiv\"},\"facultyid\":\"C70244964\",\"status\":[{\"id\":13396,\"status\":\"Submitted\",\"term\":\"Summer\",\"year\":2024,\"termid\":\"2023\\\/05\",\"listingorder\":2,\"completionorder\":2},{\"id\":13396,\"status\":\"Submitted\",\"term\":\"Fall\",\"year\":2023,\"termid\":\"2023\\\/01\",\"listingorder\":2,\"completionorder\":2}],\"userid\":\"C70244964\",\"attachments\":[],\"coauthors_list\":[\"Amir B Aazami\"],\"sort_date\":\"2023-01-01\"},{\"activityid\":5992,\"fields\":{\"Type\":\"Articles in Refereed Journals\",\"Title\":\"Almost K\\u00e4hler metrics and pp-wave spacetimes\",\"Journal Title\":\"Letters in Mathematical Physics\",\"Series Title\":\"\",\"Month \\\/ Season\":\"\",\"Year\":2022,\"Publisher\":\"\",\"Publisher City and State\":\"\",\"Publisher Country\":\"\",\"Volume\":\"112\",\"Issue Number \\\/ Edition\":\"84\",\"Page Number(s) or Number of Pages\":\"\",\"ISSN\":\"\",\"DOI\":\"\",\"CoAuthor\":null,\"URL\":\"http:\\\/\\\/arxiv.org\\\/abs\\\/2203.02825v1\",\"Description\":\"\",\"Include description in output citation\":0,\"Origin\":\"arXiv\"},\"facultyid\":\"C70244964\",\"status\":[{\"id\":5992,\"status\":\"Completed\\\/Published\",\"term\":\"Fall\",\"year\":2022,\"termid\":\"2022\\\/01\",\"listingorder\":6,\"completionorder\":6}],\"userid\":\"C70244964\",\"attachments\":[],\"coauthors_list\":[\"Amir Babak Aazami\"],\"sort_date\":\"2022-9-01\"},{\"activityid\":11323,\"fields\":{\"Type\":\"Presentations\",\"Title of Presentation\":\"On the geometry of pp-wave spacetimes\",\"Conference \\\/ Meeting Name\":\"\",\"Location of Conference \\\/ Meeting\":\"CUNY Graduate Center, New York, NY\",\"Month \\\/ Season\":\"November\",\"Year\":2022,\"Sponsoring Organization\":\"\",\"CoAuthor\":null,\"URL\":\"\",\"Description\":\"\",\"Include description in output citation\":0,\"Origin\":\"Manual\"},\"facultyid\":\"C70244964\",\"status\":[{\"id\":11323,\"status\":\"Completed\\\/Published\",\"term\":\"Fall\",\"year\":2022,\"termid\":\"2022\\\/01\",\"listingorder\":6,\"completionorder\":6}],\"userid\":\"C70244964\",\"attachments\":[],\"coauthors_list\":[\"Amir Babak Aazami\"],\"sort_date\":\"2022-11-01\"},{\"activityid\":3108,\"fields\":{\"Type\":\"Articles in Refereed Journals\",\"Title\":\"On the Einstein condition for Lorentzian 3-manifolds\",\"Journal Title\":\"Journal of Mathematical Analysis and Applications\",\"Series Title\":\"\",\"Month \\\/ Season\":\"May\\\/2021\",\"Year\":2021,\"Publisher\":\"\",\"Publisher City and State\":\"\",\"Publisher Country\":\"\",\"Volume\":\"497\",\"Issue Number \\\/ Edition\":\"2\",\"Page Number(s) or Number of Pages\":\"\",\"ISSN\":\"\",\"DOI\":\"\",\"CoAuthor\":null,\"URL\":\"http:\\\/\\\/arxiv.org\\\/abs\\\/2005.09508v2\",\"Description\":\"It is well known that in Lorentzian geometry there are no compact spherical\\nspace forms; in dimension 3, this means there are no closed Einstein\\n3-manifolds with positive Einstein constant. We generalize this fact here, by\\nproving that there are also no closed Lorentzian 3-manifolds $(M,g)$ whose\\nRicci tensor satisfies $$ \\\\text{Ric} = fg+(f-\\\\lambda)T^{\\\\flat}\\\\otimes\\nT^{\\\\flat}, $$ for any unit timelike vector field $T$, any positive constant\\n$\\\\lambda$, and any smooth function $f$ that never takes the values $0,\\\\lambda$.\\n(Observe that this reduces to the positive Einstein case when $f = \\\\lambda$.)\\nWe show that there is no such obstruction if $\\\\lambda$ is negative. Finally,\\nthe "borderline" case $\\\\lambda = 0$ is also examined: we show that if $\\\\lambda\\n= 0$ and $f > 0$, then $(M,g)$ must be isometric to $(\\\\mathbb{S}^1\\\\!\\\\times\\n\\\\!N,-dt^2\\\\oplus h)$ with $(N,h)$ a Riemannian manifold.\\n[Journal_ref: ]\",\"Include description in output citation\":0,\"Origin\":\"arXiv\"},\"facultyid\":\"C70244964\",\"status\":[{\"id\":3108,\"status\":\"Completed\\\/Published\",\"term\":\"Summer\",\"year\":2021,\"termid\":\"2020\\\/05\",\"listingorder\":6,\"completionorder\":6}],\"userid\":\"C70244964\",\"attachments\":[],\"coauthors_list\":[],\"sort_date\":\"2021-5-01\"},{\"activityid\":3111,\"fields\":{\"Type\":\"Presentations\",\"Title of Presentation\":\"Curvature and Killing vector fields on Lorentzian 3-manifolds\",\"Conference \\\/ Meeting Name\":\"X International Meeting on Lorentzian Geometry\",\"Location of Conference \\\/ Meeting\":\"Virtual\",\"Month \\\/ Season\":\"February 1-5\",\"Year\":2021,\"Sponsoring Organization\":\"University of C\\u00f3rdoba, Spain\",\"CoAuthor\":null,\"URL\":\"\",\"Description\":\"\",\"Include description in output citation\":0,\"Origin\":\"Manual\"},\"facultyid\":\"C70244964\",\"status\":[{\"id\":3111,\"status\":\"Completed\\\/Published\",\"term\":\"Spring\",\"year\":2021,\"termid\":\"2020\\\/03\",\"listingorder\":6,\"completionorder\":6}],\"userid\":\"C70244964\",\"attachments\":[],\"coauthors_list\":[\"Amir B. Aazami\"],\"sort_date\":\"2021-2-01\"},{\"activityid\":3106,\"fields\":{\"Type\":\"Articles in Refereed Journals\",\"Title\":\"K\\u00e4hler metrics via Lorentzian Geometry in dimension four\",\"Journal Title\":\"Complex Manifolds\",\"Series Title\":\"\",\"Month \\\/ Season\":\"\",\"Year\":2020,\"Publisher\":\"\",\"Publisher City and State\":\"\",\"Publisher Country\":\"\",\"Volume\":\"7\",\"Issue Number \\\/ Edition\":\"\",\"Page Number(s) or Number of Pages\":\"36-61\",\"ISSN\":\"\",\"DOI\":\"\",\"CoAuthor\":null,\"URL\":\"\",\"Description\":\"\",\"Include description in output citation\":0,\"Origin\":\"Manual\"},\"facultyid\":\"C70244964\",\"status\":[{\"id\":3106,\"status\":\"Completed\\\/Published\",\"term\":\"Fall\",\"year\":2019,\"termid\":\"2019\\\/01\",\"listingorder\":6,\"completionorder\":6}],\"userid\":\"C70244964\",\"attachments\":[],\"coauthors_list\":[\"Gideon Maschler\",\"Amir B. Aazami\"],\"sort_date\":\"2020-9-01\"},{\"activityid\":3107,\"fields\":{\"Type\":\"Articles in Refereed Journals\",\"Title\":\"Canonical K\\u00e4hler metrics on classes of Lorentzian 4-manifolds\",\"Journal Title\":\"Annals of Global Analysis and Geometry\",\"Series Title\":\"\",\"Month \\\/ Season\":\"\",\"Year\":2020,\"Publisher\":\"\",\"Publisher City and State\":\"\",\"Publisher Country\":\"\",\"Volume\":\"57\",\"Issue Number \\\/ Edition\":\"\",\"Page Number(s) or Number of Pages\":\"175-204\",\"ISSN\":\"\",\"DOI\":\"\",\"CoAuthor\":null,\"URL\":\"\",\"Description\":\"\",\"Include description in output citation\":0,\"Origin\":\"Manual\"},\"facultyid\":\"C70244964\",\"status\":[{\"id\":3107,\"status\":\"Completed\\\/Published\",\"term\":\"Fall\",\"year\":2019,\"termid\":\"2019\\\/01\",\"listingorder\":6,\"completionorder\":6}],\"userid\":\"C70244964\",\"attachments\":[],\"coauthors_list\":[\"Gideon Maschler\",\"Amir B. Aazami\"],\"sort_date\":\"2020-9-01\"},{\"activityid\":3112,\"fields\":{\"Type\":\"Presentations\",\"Title of Presentation\":\"The Ehlers-Kundt Conjecture in General Relativity\",\"Conference \\\/ Meeting Name\":\"AMS Special Session on Mathematical Physics: Some open Problems for the 21st Century\",\"Location of Conference \\\/ Meeting\":\"Denver, CO\",\"Month \\\/ Season\":\"January\",\"Year\":2020,\"Sponsoring Organization\":\"American Mathematical Society\",\"CoAuthor\":null,\"URL\":\"\",\"Description\":\"\",\"Include description in output citation\":0,\"Origin\":\"Manual\"},\"facultyid\":\"C70244964\",\"status\":[{\"id\":3112,\"status\":\"Completed\\\/Published\",\"term\":\"Spring\",\"year\":2020,\"termid\":\"2019\\\/03\",\"listingorder\":6,\"completionorder\":6}],\"userid\":\"C70244964\",\"attachments\":[],\"coauthors_list\":[\"Amir B. Aazami\"],\"sort_date\":\"2020-1-01\"}]","cu_faculty_awards_and_grants":"","cu_faculty_title":"Associate Professor, Mathematics","cu_faculty_department":"Mathematics","cu_faculty_affiliated_departments":"Mathematics","footnotes":""},"cu_faculty_group":[],"cu_faculty_department":[17],"cu_faculty_position":[],"class_list":["post-854","cu_faculty","type-cu_faculty","status-publish","has-post-thumbnail","hentry","cu_faculty_department-mathematics"],"yoast_head":"\n