Cohomogeneity one shrinking Ricci solitons: an analytic and numerical study

Details Cohomogeneity one shrinking Ricci solitons: an analytic and numerical study Cohomogeneity one shrinking Ricci solitons: an analytic and numerical study

2011-05-31

arxiv.org/abs/1105.6195v2

Mathematics

Differential Geometry

7 figures : references added

Scientific paper

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 Bohm in the Einstein case. We also carry out numerical investigations for selected orbit types.

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