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arXiv · 2201.01109

Splitting theorem of Gradient $\rho$-Einstein solitons

Absos Ali Shaikh·Prosenjit Mandal·Chandan Kumar Mondal
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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 $\rho$-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 $\rho$-Einstein soliton.

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Absos Ali Shaikh, Prosenjit Mandal, Chandan Kumar Mondal. 2022-01-04. Splitting theorem of Gradient $\rho$-Einstein solitons. https://arxiv.org/abs/2201.01109

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