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Transverse Ricci solitons on a compact foliated manifold

Seungsu Hwang, Seoung Dal Jung, Jungwoo Moon

Abstract

We investigate transverse Ricci solitons, the self-similar solutions of the transverse Ricci flow, on a compact foliated manifold. In particular, we show the relations between a taut Riemannian foliation and a transverse Ricci soliton. Moreover, we find some examples of transverse Ricci solitons.

Transverse Ricci solitons on a compact foliated manifold

Abstract

We investigate transverse Ricci solitons, the self-similar solutions of the transverse Ricci flow, on a compact foliated manifold. In particular, we show the relations between a taut Riemannian foliation and a transverse Ricci soliton. Moreover, we find some examples of transverse Ricci solitons.
Paper Structure (13 sections, 32 theorems, 156 equations)

This paper contains 13 sections, 32 theorems, 156 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Transverse Ricci solitons
  4. General facts from transverse Ricci flow
  5. The equation of transverse Ricci solitons
  6. Transverse Ricci solitons and transverse curvature functionals
  7. Properties of transverse Ricci solitons
  8. General formulae
  9. A shrinking transverse Ricci soliton
  10. A steady transverse Ricci soliton
  11. Transverse Ricci solitons on a taut foliation
  12. An expanding transverse Ricci soliton
  13. Examples of transverse Ricci solitons

Key Result

Theorem 1.1

Per Every Ricci soliton on a compact manifold is a gradient Ricci soliton.

Theorems & Definitions (69)

  • Theorem 1.1
  • Theorem 1.2
  • Theorem 1.3
  • Remark 1.4
  • Proposition 2.1
  • Theorem 2.2
  • Theorem 2.3
  • Corollary 2.4
  • Proposition 3.1
  • Remark 3.2
  • ...and 59 more