Splitting theorem of Gradient ρ-Einstein solitons

2022/01/04 by Shaikh, Absos Ali, Mandal, Prosenjit, Mondal, Chandan Kumar
#35K15 #53C21 #53C25 #53C44 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2201.01109

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 ρ-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 ρ-Einstein soliton.

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