Killing Fields on Compact m-Quasi-Einstein Manifolds

Autor:	Cochran, Eric
Rok vydání:	2024
Předmět:	Mathematics - Differential Geometry
Druh dokumentu:	Working Paper
Popis:	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. Comment: 9 pages, equations reformatted, typos fixed, remark added. To appear in the Proceedings of the AMS
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2404.17090 Zobrazit plný text záznamu View this record from Arxiv