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arXiv · 2608.01594

Holomorphic functions on complete Hermitian manifolds with flat Chern connection

Zeqing Miao·Hanyu Wu·Bo Yang
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Abstract

A classical result of Boothby states that any compact Hermitian manifold with flat Chern connection is covered by a complex Lie group. In this work, we prove a sharp generalization: the universal cover of any complete Hermitian manifold with vanishing Chern curvature and torsion of sublinear growth is holomorphically isometric to a complex Lie group equipped with a left-invariant metric. The proof relies on a new gradient estimate for holomorphic functions on complete Hermitian manifolds with nonnegative second Ricci curvature. Combining this estimate with methods from sub-Riemannian geometry, we establish quantitative characterizations of function theory on these manifolds.

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Zeqing Miao, Hanyu Wu, Bo Yang. 2026-08-03. Holomorphic functions on complete Hermitian manifolds with flat Chern connection. https://arxiv.org/abs/2608.01594

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