On Four-Dimensional Anti-self-dual Gradient Ricci Solitons

Xiuxiong Chen; Yuanqi Wang

doi:10.1007/s12220-014-9471-8

On Four-Dimensional Anti-self-dual Gradient Ricci Solitons

Xiuxiong Chen
, Yuanqi Wang

Mathematics

University of California at Santa Barbara

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

51 Scopus citations

Abstract

In this note we prove that any four-dimensional half-conformally flat gradient steady Ricci soliton must be either isometric to the Bryant’s soliton (up to a scaling), or with zero Ricci curvature. We also classify four-dimensional half-conformally flat gradient shrinking Ricci solitons.

Original language	English
Pages (from-to)	1335-1343
Number of pages	9
Journal	Journal of Geometric Analysis
Volume	25
Issue number	2
DOIs	https://doi.org/10.1007/s12220-014-9471-8
State	Published - Apr 2015

Keywords

Anti-self-dual
Ricci solitons

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10.1007/s12220-014-9471-8

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title = "On Four-Dimensional Anti-self-dual Gradient Ricci Solitons",

abstract = "In this note we prove that any four-dimensional half-conformally flat gradient steady Ricci soliton must be either isometric to the Bryant{\textquoteright}s soliton (up to a scaling), or with zero Ricci curvature. We also classify four-dimensional half-conformally flat gradient shrinking Ricci solitons.",

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author = "Xiuxiong Chen and Yuanqi Wang",

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AU - Wang, Yuanqi

PY - 2015/4

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AB - In this note we prove that any four-dimensional half-conformally flat gradient steady Ricci soliton must be either isometric to the Bryant’s soliton (up to a scaling), or with zero Ricci curvature. We also classify four-dimensional half-conformally flat gradient shrinking Ricci solitons.

KW - Anti-self-dual

KW - Ricci solitons

UR - https://www.scopus.com/pages/publications/84944180695

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DO - 10.1007/s12220-014-9471-8

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JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 2

ER -

On Four-Dimensional Anti-self-dual Gradient Ricci Solitons

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Keywords

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