Asian Journal of Mathematics
Volume 17 (2013)
Cohomogeneity one shrinking Ricci solitons: an analytic and numerical study
Pages: 33 – 62
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.
gradient Ricci solitons, shrinkers, winding number, non-existence, numerics
2010 Mathematics Subject Classification