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.

中文翻译：

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普通Ricci孤子的特征

在黎氏孤子的几何学中，找到平凡的孤子的特征是一个重要的问题。在本文中，我们发现了平凡的Ricci孤子的几个特征。首先，在完全收缩的Ricci孤子上，我们证明了满足一定不等式的标量曲率给出了琐碎的Ricci孤子的特征。然后，表明具有测地线流动和满足某些不等式的势场长度的势场给出了平凡的Ricci孤子的另一个特征。最后，我们证明了满足不等式的恒定长度的势场给出了平凡的Ricci孤子的表征。