Asian Journal of Mathematics

Cohomogeneity one shrinking Ricci solitons: An analytic and numerical study

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

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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

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

First available in Project Euclid: 8 November 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Gradient Ricci solitons shrinkers winding number non-existence numerics


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.

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