Painlev\'e analysis of Ricci solitons over warped products
Differential Geometry
2018-03-01 v1
Abstract
We carry out a Painlev\'e 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 K\"ahler 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 particularly distinguished. The case with two factors each of dimension 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.
Keywords
Cite
@article{arxiv.1802.10227,
title = {Painlev\'e analysis of Ricci solitons over warped products},
author = {Alejandro Betancourt de la Parra},
journal= {arXiv preprint arXiv:1802.10227},
year = {2018}
}