On the rigidity of ℂℙ2n × ℂℙ1

We revisit Koiso’s original examples of rigid infinitesimally deformable Einstein metrics. We show how to compute Koiso’s obstruction to the integrability of the infinitesimal deformations on using completely elementary complex differential geometry.

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Bibliographic Details
Published in:	Complex manifolds (Warsaw, Poland) Vol. 12; no. 1; pp. 2066 - 2098
Main Author:	Hall, Stuart James
Format:	Journal Article
Language:	English
Published:	De Gruyter 01.02.2025
Subjects:	32Q20 53C25 53C55 deformations Einstein manifolds
ISSN:	2300-7443
Online Access:	Get full text
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Description
Summary:	We revisit Koiso’s original examples of rigid infinitesimally deformable Einstein metrics. We show how to compute Koiso’s obstruction to the integrability of the infinitesimal deformations on using completely elementary complex differential geometry.
ISSN:	2300-7443
DOI:	10.1515/coma-2024-0008