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On Ricci solitons whose potential is convex

Authors
  • Mondal, Chandan Kumar1
  • Shaikh, Absos Ali1
  • 1 University of Burdwan, Golapbag, Burdwan, 713 104, India , Golapbag (India)
Type
Published Article
Journal
Proceedings - Mathematical Sciences
Publisher
Springer India
Publication Date
Sep 16, 2020
Volume
130
Issue
1
Identifiers
DOI: 10.1007/s12044-020-00577-5
Source
Springer Nature
Keywords
License
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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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