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

Year 2023, Volume: 16 Issue: 1, 266 - 271, 30.04.2023

Rahul Poddar Balasubramanian Subramanian R. Sharma

https://doi.org/10.36890/iejg.1286128

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 $(n-1)$-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

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