Splitting theorem of Gradient $\rho$-Einstein solitons
Differential Geometry
2022-01-05 v1
Abstract
In this paper, we have proved a weighted Laplacian comparison of distance function for manifolds with Bakry-\'Emery curvature bounded from below. Next, we have shown that a gradient -Einstein soliton with a bounded integral condition on Ricci curvature splits off a line isometrically. Moreover, using this result, we have established some boundedness conditions on scalar curvature of gradient -Einstein soliton.
Keywords
Cite
@article{arxiv.2201.01109,
title = {Splitting theorem of Gradient $\rho$-Einstein solitons},
author = {Absos Ali Shaikh and Prosenjit Mandal and Chandan Kumar Mondal},
journal= {arXiv preprint arXiv:2201.01109},
year = {2022}
}
Comments
10 pages