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arXiv · 2112.00488

Mean curvature positivity and rational connectedness

Chao Li·Chuanjing Zhang·Xi Zhang
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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 K\"ahler manifold is projective and rationally connected if and only if its holomorphic tangent bundle is mean curvature positive.

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Chao Li, Chuanjing Zhang, Xi Zhang. 2021-12-01. Mean curvature positivity and rational connectedness. https://arxiv.org/abs/2112.00488

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