Asian Journal of Mathematics

Cohomogeneity one shrinking Ricci solitons: An analytic and numerical study

Andrew S. Dancer, Stuart J. Hall, and McKenzie Y. Wang

Full-text: Open access

Abstract

We use analytical and numerical methods to investigate the equations for cohomogeneity one shrinking gradient Ricci solitons. We show the existence of a winding number for this system around the subvariety of phase space corresponding to Einstein solutions and obtain some estimates for it. We prove a non-existence result for certain orbit types, analogous to that of Böhm in the Einstein case. We also carry out numerical investigations for selected orbit types.

Article information

Source
Asian J. Math., Volume 17, Number 1 (2013), 33-62.

Dates
First available in Project Euclid: 8 November 2013

Permanent link to this document
https://projecteuclid.org/euclid.ajm/1383923435

Mathematical Reviews number (MathSciNet)
MR3038724

Zentralblatt MATH identifier
1280.53044

Subjects
Primary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.) 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)

Keywords
Gradient Ricci solitons shrinkers winding number non-existence numerics

Citation

Dancer, Andrew S.; Hall, Stuart J.; Wang, McKenzie Y. Cohomogeneity one shrinking Ricci solitons: An analytic and numerical study. Asian J. Math. 17 (2013), no. 1, 33--62. https://projecteuclid.org/euclid.ajm/1383923435


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