Mean curvature positivity and rational connectedness

2021/12/01 by Chao Li, Li, Chao, Chuanjing Zhang +3
Mathematics · #Geometry and complex manifolds #Algebraic Geometry and Number Theory #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2112.00488

Abstract

In this paper, we use Uhlenbeck-Yau's continuity method to establish the correspondence between the mean curvature positivity and the HN-positivity on holomorphic vector bundles over compact Hermitian manifolds. As its application, we get a differential geometric criterion for rational connectedness, i.e. we prove that a compact Kähler manifold is projective and rationally connected if and only if its holomorphic tangent bundle is mean curvature positive.

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