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On the structure of gradient Yamabe solitons

Huai-Dong Cao, Xiaofeng Sun, Yingying Zhang

Abstract

We show that every complete nontrivial gradient Yamabe soliton admits a special global warped product structure with a one-dimensional base. Based on this, we prove a general classification theorem for complete nontrivial locally conformally flat gradient Yamabe solitons.

On the structure of gradient Yamabe solitons

Abstract

We show that every complete nontrivial gradient Yamabe soliton admits a special global warped product structure with a one-dimensional base. Based on this, we prove a general classification theorem for complete nontrivial locally conformally flat gradient Yamabe solitons.

Paper Structure

This paper contains 3 sections, 4 theorems, 36 equations.

Table of Contents

  1. The results
  2. Warped product structures of complete gradient Yamabe solitons
  3. Classification of locally conformally flat Yamabe solitons

Key Result

Theorem 1.1

(Daskalopoulos-Sesum DS) All complete locally conformally flat gradient Yamabe solitons with positive sectional curvature $K>0$ are rotationally symmetric.

Theorems & Definitions (11)

  • Theorem 1.1
  • Theorem 1.2
  • Remark 1.1
  • Remark 1.2
  • Remark 1.3
  • Proposition 2.1
  • Remark 2.1
  • Remark 2.2
  • Lemma 2.1
  • Remark 2.3
  • ...and 1 more