Complete non-compact gradient Ricci solitons with nonnegative Ricci curvature
Differential Geometry
2013-12-05 v1
Abstract
In this paper, we give a delay estimate of scalar curvature for a complete non-compact expanding (or steady) gradient Ricci soliton with nonnegative Ricci curvature. As an application, we prove that any complete non-compact expanding (or steady) gradient K\"{a}hler-Ricci solitons with positively pinched Ricci curvature should be Ricci flat. The result answers a question in case of K\"{a}hler-Ricci solitons proposed by Chow, Lu and Ni in a book.
Keywords
Cite
@article{arxiv.1312.1216,
title = {Complete non-compact gradient Ricci solitons with nonnegative Ricci curvature},
author = {Yuxing Deng and Xiaohua Zhu},
journal= {arXiv preprint arXiv:1312.1216},
year = {2013}
}
Comments
18 pages