Asymptotic behavior of positively curved steady Ricci Solitons

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 Kähler-Ricci soliton with non-negative sectional curvature must be flat.

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