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arXiv · 2306.16174

On weak and strict relatives K\"ahler manifolds

Giovanni Placini
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Abstract

We study K\"ahler manifolds that are (weak) relatives, that is, K\"ahler manifolds which share a (locally isometric) submanifold. In particular, we prove that if two K\"ahler manifolds are weak relatives and one of them is projective, then they are relatives. Moreover, we introduce the notion of strict relatives K\"ahler manifolds and provide several nontrivial examples.

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Giovanni Placini. 2023-06-28. On weak and strict relatives K\"ahler manifolds. https://doi.org/10.1215/21562261-2024-0039

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