Some rigidity results for noncompact gradient steady Ricci solitons and Ricci-flat manifolds

Fei He

doi:10.1016/j.difgeo.2017.04.007

Some rigidity results for noncompact gradient steady Ricci solitons and Ricci-flat manifolds

Fei He

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Gradient steady Ricci solitons are natural generalizations of Ricci-flat manifolds. In this article, we prove a curvature gap theorem for gradient steady Ricci solitons with nonconstant potential functions; and a curvature gap theorem for Ricci-flat manifolds, removing the volume growth assumptions in known results.

Original language	English (US)
Pages (from-to)	181-200
Number of pages	20
Journal	Differential Geometry and its Application
Volume	52
DOIs	https://doi.org/10.1016/j.difgeo.2017.04.007
State	Published - Jun 1 2017

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© 2017 Elsevier B.V.

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title = "Some rigidity results for noncompact gradient steady Ricci solitons and Ricci-flat manifolds",

abstract = "Gradient steady Ricci solitons are natural generalizations of Ricci-flat manifolds. In this article, we prove a curvature gap theorem for gradient steady Ricci solitons with nonconstant potential functions; and a curvature gap theorem for Ricci-flat manifolds, removing the volume growth assumptions in known results.",

author = "Fei He",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier B.V.",

year = "2017",

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day = "1",

doi = "10.1016/j.difgeo.2017.04.007",

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AB - Gradient steady Ricci solitons are natural generalizations of Ricci-flat manifolds. In this article, we prove a curvature gap theorem for gradient steady Ricci solitons with nonconstant potential functions; and a curvature gap theorem for Ricci-flat manifolds, removing the volume growth assumptions in known results.

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DO - 10.1016/j.difgeo.2017.04.007

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AN - SCOPUS:85018391936

SN - 0926-2245

VL - 52

SP - 181

EP - 200

JO - Differential Geometry and its Application

JF - Differential Geometry and its Application

ER -

Some rigidity results for noncompact gradient steady Ricci solitons and Ricci-flat manifolds

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