Characterizations of Trivial Ricci Solitons

Sharief Deshmukh, Nasser Bin Turki and Hana Alsodais

Advances in Mathematical Physics, 2020, vol. 2020, issue 1

Abstract: Finding characterizations of trivial solitons is an important problem in geometry of Ricci solitons. In this paper, we find several characterizations of a trivial Ricci soliton. First, on a complete shrinking Ricci soliton, we show that the scalar curvature satisfying a certain inequality gives a characterization of a trivial Ricci soliton. Then, it is shown that the potential field having geodesic flow and length of potential field satisfying certain inequality gives another characterization of a trivial Ricci soliton. Finally, we show that the potential field of constant length satisfying an inequality gives a characterization of a trivial Ricci soliton.

Date: 2020
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https://doi.org/10.1155/2020/9826570

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2020:y:2020:i:1:n:9826570

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