Painlevé analysis of Ricci solitons over warped products

Abstract

We carry out a Painlevé analysis to find the cases where the cohomogeneity one steady Ricci soliton equation can be integrable. We concentrate on two classes of solitons: warped products and complex line bundles over a Fano Kähler Einstein base. For warped products, the analysis singles out the case with one factor where the dimension of the hypersurface is a perfect square, with the $n=4$ particularly distinguished. The case with two factors each of dimension $2$ is also singled out by the analysis. In the case of complex line bundles, a 1-parameter family is singled out for every even dimension.

References in corpus (2)

• Cohomogeneity one Ricci Solitons from Hopf Fibrations
• A family of non-collapsed steady Ricci solitons in even dimensions greater or equal to four