English

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}
}

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18 pages