Classification of gradient steady Ricci solitons with linear curvature decay

Yuxing Deng; Xiaohua Zhu

doi:10.1007/s11425-019-1548-0

Classification of gradient steady Ricci solitons with linear curvature decay

Yuxing Deng^*, Xiaohua Zhu

^*Corresponding author for this work

School of Mathematics and Statistics

Peking University

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

10 Citations (Scopus)

Abstract

In this paper, we study steady Ricci solitons with a linear decay of sectional curvature. In particular, we give a complete classification of 3-dimensional steady Ricci solitons and 4-dimensional κ-noncollapsed steady Ricci solitons with non-negative sectional curvature under the linear curvature decay.

Original language	English
Pages (from-to)	135-154
Number of pages	20
Journal	Science China Mathematics
Volume	63
Issue number	1
DOIs	https://doi.org/10.1007/s11425-019-1548-0
Publication status	Published - 1 Jan 2020

Keywords

53C25
53C55
58J05
Ricci flow
rotational symmetry
steady Ricci solitons

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10.1007/s11425-019-1548-0

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title = "Classification of gradient steady Ricci solitons with linear curvature decay",

abstract = "In this paper, we study steady Ricci solitons with a linear decay of sectional curvature. In particular, we give a complete classification of 3-dimensional steady Ricci solitons and 4-dimensional κ-noncollapsed steady Ricci solitons with non-negative sectional curvature under the linear curvature decay.",

keywords = "53C25, 53C55, 58J05, Ricci flow, rotational symmetry, steady Ricci solitons",

author = "Yuxing Deng and Xiaohua Zhu",

note = "Publisher Copyright: {\textcopyright} 2019, Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature.",

year = "2020",

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T1 - Classification of gradient steady Ricci solitons with linear curvature decay

AU - Deng, Yuxing

AU - Zhu, Xiaohua

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AB - In this paper, we study steady Ricci solitons with a linear decay of sectional curvature. In particular, we give a complete classification of 3-dimensional steady Ricci solitons and 4-dimensional κ-noncollapsed steady Ricci solitons with non-negative sectional curvature under the linear curvature decay.

KW - 53C25

KW - 53C55

KW - 58J05

KW - Ricci flow

KW - rotational symmetry

KW - steady Ricci solitons

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DO - 10.1007/s11425-019-1548-0

M3 - Article

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SN - 1674-7283

VL - 63

SP - 135

EP - 154

JO - Science China Mathematics

JF - Science China Mathematics

IS - 1

ER -

Classification of gradient steady Ricci solitons with linear curvature decay

Abstract

Keywords

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