- International Electronic Journal of Geometry
- Vol: 16 Issue: 1
- Rigidity Results On Generalized m-Quasi Einstein Manifolds with Associated Affine Killing Vector Fie...
Rigidity Results On Generalized m-Quasi Einstein Manifolds with Associated Affine Killing Vector Field.
Authors : Rahul Poddar, Balasubramanian Subramanian, R. Sharma
Pages : 266-271
Doi:10.36890/iejg.1286128
View : 7 | Download : 2
Publication Date : 2023-04-30
Article Type : Research
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