Rigidity Results On Generalized m-Quasi Einstein Manifolds with Associated Affine Killing Vector Field.

Authors : Rahul PODDAR, Balasubramanian SUBRAMANİAN, R. SHARMA

Pages : 266-271

Doi:10.36890/iejg.1286128

View : 10 | Download : 4

Publication Date : 2023-04-30

Article Type : Research Paper

Abstract :We study a non-trivial generalized $m$-quasi Einstein manifold $M$ with finite $m$ and associated divergence-free affine Killing vector field, and show that $M$ reduces to an $m$-quasi Einstein manifold. In addition, if $M$ is complete, then it splits as the product of a line and an $insert ignore into journalissuearticles values(n-1);$-dimensional negatively Einstein manifold. Finally, we show that the same result holds for a complete non-trivial $m$-quasi Einstein manifold $M$ with finite $m$ and associated affine Killing vector field.
Keywords : Generalized m quasi Einstein manifold, affine Killing vector field, Einstein manifold, Ricci almost soliton