On the Rigidity of ${\mathbb{CP}}^{2n}\times {\mathbb{CP}}^1$

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 ${\mathbb{CP}}^n\times {\mathbb{CP}}^1$ using completely elementary complex differential geometry.

13 pages