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arXiv · 1802.10227

Painlev\'e analysis of Ricci solitons over warped products

Alejandro Betancourt de la Parra
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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 $n=4$ 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.

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Alejandro Betancourt de la Parra. 2018-02-28. Painlev\'e analysis of Ricci solitons over warped products. https://arxiv.org/abs/1802.10227

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