Locally rigid implies globally rigid in Kahler geometry

Mu-Lin Li

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arXiv · 2604.26329

Locally rigid implies globally rigid in Kahler geometry

Mu-Lin Li

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Abstract

In this paper, we study the rigidity properties of compact Kahler manifolds. Given a smooth family of compact Kahler manifolds X over the unit disk, we show that all the fibers are mutually isomorphic if the family is locally trivial at a point t_1 and the fiber X_{t_1} is non-uniruled. This proves that the locally rigid implies the global rigid in Kahler. It also can be used to prove the so called global non-deformability for non-uniruled Kahler manifolds under Kahler morphisms.

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BibTeX RIS

Mu-Lin Li. 2026-04-29. Locally rigid implies globally rigid in Kahler geometry. https://arxiv.org/abs/2604.26329

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