On the rigidity of ℂℙ2n × ℂℙ1

Abstract

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 CP2n×CP1{{\mathbb{CP}}}^{2n}\times {{\mathbb{CP}}}^{1} using completely elementary complex differential geometry.

Keywords

• einstein manifolds
• deformations
• 53c25
• 53c55
• 32q20