• On Ricci solitons whose potential is convex

• Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/130/0055

• Keywords

Ricci soliton; scalar curvature; Ricci flat; convex function; critical point; Riemannian manifold.

• Abstract

In this paper, we consider theRicci 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 curvaturehas at most one critical point.

• Author Affiliations

1. Department of Mathematics, University of Burdwan, Golapbag, Burdwan 713 104, India

• Proceedings – Mathematical Sciences

Volume 130, 2020
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