Mean curvature positivity and rational connectedness
Differential Geometry
2024-12-11 v3
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.
Cite
@article{arxiv.2112.00488,
title = {Mean curvature positivity and rational connectedness},
author = {Chao Li and Chuanjing Zhang and Xi Zhang},
journal= {arXiv preprint arXiv:2112.00488},
year = {2024}
}