On the Rigidity of \mathbbCP²ⁿ× \mathbbCP¹

2024/08/29 by Stuart James Hall, Hall, Stuart James
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2408.16689

openalex publication_date 2024/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \mathbbCPⁿ× \mathbbCP¹ using completely elementary complex differential geometry.

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