2024/04/26 by Eric Cochran, Cochran, Eric · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2404.17090
openalex publication_date 2024/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that given a compact, connected m-quasi Einstein manifold (M,g,X) without boundary, the potential vector field X is Killing if and only if (M, g) has constant scalar curvature. This extends a result of Bahuaud-Gunasekaran-Kunduri-Woolgar, where it is shown that X is Killing if X is incompressible. We also provide a sufficient condition for a compact, non-gradient m-quasi Einstein metric to admit a Killing field. We do this by following a technique of Dunajski and Lucietti, who prove that a Killing field always exists in this case when m=2. This condition provides an alternate proof of the aforementioned result of Bahuaud-Gunasekaran-Kunduri-Woolgar. This alternate proof works in the m = -2 case as well, which was not covered in the original proof.