Nonexistence of nontrivial quasi-Einstein metrics

Kodai Mathematical Journal

Yawei Chu¹ 

[1] School of Mathematics and Computational Science Fuyang Teachers College

关键词: Nonexistence;    Quasi-Einstein;    Gradient Ricci solitons;    Gradient estimate;    Smooth metric measure space;   

DOI  :  10.2996/kmj/1341401057

学科分类：数学（综合）

来源: Tokyo Institute of Technology, Department of Mathematics

【 摘 要 】

References(18)Let (Mn, g, e–f dvolg) be a smooth metric measure space of dimension n. In this note, we first prove a nonexistence result for Mn with the Bakry-Émery Ricci tensor is bounded from below. Then we show that f ∈ L∞ (Mn, e–f dvol) and |∇f| ∈ L∞ (Mn, e–f dvol) are equivalent for complete gradient shrinking Ricci solitons. Furthermore, we prove that there is no non-Einstein shrinking soliton when the normalized function $\tilde f$ is non-positive.

【 授权许可】

Unknown