Characterizations of Trivial Ricci Solitons

Abstract EN

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.