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Complete Ricci solitons via estimates on the soliton potential

Matthias Wink

Abstract

In this paper a growth estimate on the soliton potential is shown for a large class of cohomogeneity one manifolds. This is used to construct continuous families of complete steady and expanding Ricci solitons in the set-ups of Lü-Page-Pope and Dancer-Wang. It also provides a different approach to the two summands system which applies to all known geometric examples.

Complete Ricci solitons via estimates on the soliton potential

Abstract

In this paper a growth estimate on the soliton potential is shown for a large class of cohomogeneity one manifolds. This is used to construct continuous families of complete steady and expanding Ricci solitons in the set-ups of Lü-Page-Pope and Dancer-Wang. It also provides a different approach to the two summands system which applies to all known geometric examples.

Paper Structure

This paper contains 10 sections, 21 theorems, 93 equations.

Table of Contents

  1. Growth of the soliton potential
  2. Preliminaries
  3. An estimate on the soliton potential
  4. Preparation for the proof: Scalar curvature of homogeneous spaces
  5. Proof of the growth estimate theorem \ref{['MainGrowthEstimateTheorem']}
  6. Applications
  7. Revision of the two summands case
  8. Generalisations of the circle bundle case
  9. The Dancer-Wang set-up
  10. The Lü-Page-Pope set-up

Key Result

Theorem A

Let $L$ be the total space of a complex line bundle over a product of Fano Kähler Einstein manifolds with $m \geq 1$ factors whose Euler class is a rational linear combination of the first Chern classes of the base manifolds. Then there exist an $m$-parameter family of complete non-trivial steady an

Theorems & Definitions (48)

  • Theorem A
  • Theorem B
  • Theorem C
  • Remark 1.1
  • Proposition 1.2
  • proof
  • Proposition 1.3
  • Theorem 1.4
  • Remark 1.5
  • Proposition 1.6
  • ...and 38 more