On weak and strict relatives Kähler manifolds

2023/06/28 by Giovanni Placini, Placini, Giovanni · 1 citation
Mathematics · #32Q15 #53B35 (Secondary) #53C42 (Primary) 53C24 #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2306.16174

openalex publication_date 2023/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

Abstract

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

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• Universal embeddings of flag manifolds and rigidity phenomena

Related

• Kahler manifolds and their relatives
• Strongly not relatives Kaehler manifolds
• Remarks on Weakly p-Kähler hyperbolic manifolds
• Relative K-stability for Kähler manifolds
• Universal embeddings of flag manifolds and rigidity phenomena