Gradient steady Kahler Ricci solitons with non-negative Ricci curvature and integrable scalar curvature

DOI10.4310/CAG.2022.V30.N2.A2arXiv1908.10445MaRDI QIDQ6324294

Publication date: 27 August 2019

Abstract: We study the non Ricci flat gradient steady K"{a}hler Ricci soliton with non-negative Ricci curvature and weak integrability condition of the scalar curvature

S

, namely

u n d e r l i n e {l i m}_{r o i n f t y} r^{- 1} i n t_{B_{r}} S = 0

, and show that it is a quotient of

S i g m a i m e s m a t h b b C^{n - 1 - k} i m e s N^{k}

, where

S i g m a

and

N

denote the Hamilton's cigar soliton and some compact K"{a}hler Ricci flat manifold respectively. As an application, we prove that any non Ricci flat gradient steady K"{a}hler Ricci soliton with

R i c g e q 0

, together with subquadratic volume growth or

l i m s u p_{r o i n f t y} r S < 1

must have universal covering space isometric to

S i g m a i m e s m a t h b b C^{n - 1 - k} i m e s N^{k}

.

Mathematics Subject Classification ID

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