发表机构
Fudan University（复旦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究将埃尔米特流形的陈挠率视为全纯切丛上的斜对称复双线性乘积，证明类陈-凯勒紧致连通埃尔米特流形的挠率乘积满足雅可比恒等式，强拟正陈全纯截面曲率时挠率李代数幂零且为零，进而推出度量为凯勒度量，还构造了非单连通非有理连通Hopf曲面的正实双截曲率度量。
AI 中文摘要
我们将埃尔米特流形的陈挠率视为其全纯切丛上的斜对称复双线性乘积。对于紧致连通的类陈-凯勒（Chern--Kähler-like）埃尔米特流形，我们证明该乘积逐点满足雅可比恒等式。若陈全纯截面曲率为强拟正，我们证明所得挠率李代数幂零且必为零，因此该度量是凯勒（Kähler）度量，对应的复流形是射影且有理连通的。对一般埃尔米特流形，我们在Hopf曲面上构造了一个具有正实双截曲率的度量，该曲面既非单连通也非有理连通。
英文摘要
We regard the Chern torsion of a Hermitian manifold as a skew-symmetric complex-bilinear product on its holomorphic tangent bundle. For a compact connected Chern--Kähler-like Hermitian manifold, we prove that this product satisfies the Jacobi identity pointwise. If, in addition, the Chern holomorphic sectional curvature is strongly quasi-positive, we show that the resulting torsion Lie algebra is nilpotent and must be abelian. Consequently, the metric is Kähler. The underlying complex manifold is therefore projective and rationally connected. For general Hermitian manifolds, we construct a metric with positive real bisectional curvature on a Hopf surface which is neither simply connected nor rationally connected.
Comments24 pages, notation revised
