English

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 n=4n=4 particularly distinguished. The case with two factors each of dimension 22 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}
}