On Ricci solitons whose potential is convex

2019/08/22 by Mondal, Chandan Kumar, Shaikh, Absos Ali
#53C44 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1908.08303

Abstract

In this paper we consider the Ricci curvature of a Ricci soliton. In particular, we have showed that a complete gradient Ricci soliton with non-negative Ricci curvature possessing a non-constant convex potential function having finite weighted Dirichlet integral satisfying an integral condition is Ricci flat and also it isometrically splits a line. We have also proved that a gradient Ricci soliton with non-constant concave potential function and bounded Ricci curvature is non-shrinking and hence the scalar curvature has at most one critical point.

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