具有平坦陈联络的完备埃尔米特流形上的全纯函数
Holomorphic functions on complete Hermitian manifolds with flat Chern connection
浏览论文内容
中文总结 AI 辅助
本文推广Boothby的经典结果，证明陈曲率为零且挠率次线性增长的完备埃尔米特流形的万有覆盖与带左不变度量的复李群全纯等距，通过新梯度估计结合次黎曼几何方法完成证明并得到函数论定量刻画。
中文摘要 AI 辅助
Boothby的经典结果指出，任何具有平坦陈联络的紧埃尔米特流形都可被一个复李群覆盖。在本研究中，我们证明了一个尖锐的推广结论：任何陈曲率为零且挠率次线性增长的完备埃尔米特流形的万有覆盖，与配备左不变度量的复李群全纯等距。该证明依赖于具有非负第二里奇曲率的完备埃尔米特流形上全纯函数的新梯度估计，结合次黎曼几何方法，我们建立了这类流形上函数论的定量刻画。
英文摘要
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.
