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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The authors would like to thank the unknown referee for carefully reading the paper and for thoughtful criticism of the manuscript, which helped improve the manuscript considerably.
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Mondal, C.K., Shaikh, A.A. On Ricci solitons whose potential is convex. Proc Math Sci 130, 55 (2020). https://doi.org/10.1007/s12044-020-00577-5
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DOI: https://doi.org/10.1007/s12044-020-00577-5