Remarks on complete non-compact gradient Ricci expanding solitons

Kodai Mathematical Journal

Dezhong Chen²  Li Ma¹ 

[1] Department of Mathematical Sciences Tsinghua University;Department of Mathematics and Statistics McMaster University

关键词: Ricci flow;    expanding soliton;   

DOI  :  10.2996/kmj/1278076334

学科分类：数学（综合）

来源: Tokyo Institute of Technology, Department of Mathematics

【 摘 要 】

References(12)In this paper, we study gradient Ricci expanding solitons (X,g) satisfyingRc = cg + D2f,where Rc is the Ricci curvature, c < 0 is a constant, and D2f is the Hessian of the potential function f on X. We show that for a gradient expanding soliton (X,g) with non-negative Ricci curvature, the scalar curvature R has at most one maximum point on X, which is the only minimum point of the potential function f. Furthermore, R > 0 on X unless (X,g) is Ricci flat. We also show that there is exponentially decay for scalar curvature on a complete non-compact expanding soliton with its Ricci curvature being ε-pinched.

【 授权许可】

Unknown