Asian Journal of Mathematics

Volume 17 (2013)

Number 1

Cohomogeneity one shrinking Ricci solitons: an analytic and numerical study

Pages: 33 – 62

DOI: https://dx.doi.org/10.4310/AJM.2013.v17.n1.a3

Authors

Andrew S. Dancer (Jesus College, Oxford University, United Kingdom)

Stuart J. Hall (Department of Applied Computing, University of Buckingham, United Kingdom)

McKenzie Y. Wang (Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada)

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.

Keywords

gradient Ricci solitons, shrinkers, winding number, non-existence, numerics

2010 Mathematics Subject Classification

53C25, 53C40

Published 21 March 2013