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Triviality and Rigidity of Almost Riemann Solitons

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Abstract

In this paper, we study some triviality and rigidity results of Riemann soliton. First, we derive some sufficient conditions for which an almost Riemann soliton is trivial. In particular, we prove that any compact almost Riemann soliton with constant scalar curvature has constant sectional curvature. Next, we prove some rigidity results for gradient Riemann solitons. Precisely, we prove that a non-trivial gradient Riemann soliton is locally isometric to a warped product \(( I \times F, \textrm{d}t^2 + f(t)^2g_{F})\), where \(\nabla \sigma \ne 0\).

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The author is very much thankful to the Reviewer for some valuable suggestions and comments.

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  1. Department of Mathematics, Chandernagore College, Hooghly, W.B., 712 136, India

    Amalendu Ghosh

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Ghosh, A. Triviality and Rigidity of Almost Riemann Solitons. Mediterr. J. Math. 21, 81 (2024). https://doi.org/10.1007/s00009-024-02620-5

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