Research profile

Alejandro Betancourt de la Parra

Works on Kähler–Einstein & K-stability, rotational symmetry & warped products and Einstein metrics.

NP-RC-945648

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Kähler–Einstein & K-stabilityRotational symmetry & warped productsEinstein metricsHomogeneous spacesKähler geometryRicci solitons

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Their work in this field since 2016, with the older papers the site recommends. Titles open each paper's page, with its abstract, PDF and HTML versions; Connections shows the papers closest to it. The arXiv listing has the complete record.

2018

math.DGarXiv:1802.10227

Painlevé analysis of Ricci solitons over warped products

Alejandro Betancourt de la Parra

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 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.

Ricci solitonsEinstein metricsKähler geometryHomogeneous spacesRotational symmetry & warped productsKähler–Einstein & K-stability
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