Asymptotic behavior of positively curved steady Ricci Solitons

Yuxing Deng; Xiaohua Zhu

Asymptotic behavior of positively curved steady Ricci Solitons

Differential Geometry 2017-01-17 v3

Authors: Yuxing Deng , Xiaohua Zhu

Abstract

In this paper, we analyze the asymptotic behavior of $\kappa$ -noncollapsed and positively curved steady Ricci solitons and prove that any $n$ -dimensional $\kappa$ -noncollapsed steady K\"ahler-Ricci soliton with non-negative sectional curvature must be flat.

Keywords

steady Ricci solitons asymptotic behavior kappa-noncollapsed positive curvature Kähler-Ricci soliton sectional curvature flatness

Cite

@article{arxiv.1507.04802,
  title  = {Asymptotic behavior of positively curved steady Ricci Solitons},
  author = {Yuxing Deng and Xiaohua Zhu},
  journal= {arXiv preprint arXiv:1507.04802},
  year   = {2017}
}

Comments

This is a final version. We added some details in the proofs of Proposition 4.3 and Corollary 4.5

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