Relating the curvature tensor and the complex Jacobi operator of an almost Hermitian manifold

The Hermitian Connection and the Jacobi Fields of a Complex Finsler Manifold

It is proved that all invariant functions of a complex Finsler manifold can be totally recovered from the torsion and curvature of the connection introduced by Kobayashi for holomorphic vector bundles with complex Finsler structures. Equations of the geodesics and Jacobi fields of a generic complex Finsler manifold, expressed by means Kobayashi's connection, are also derived.

厄米矩阵单纯形上的雅可比多项式与部分旗流形上的带状球函数

Jacobi polynomials on the simplex of Hermitian matrices and zonal spherical functions on partial flag manifolds

研究部分旗流形上拉普拉斯 - 贝尔特拉米算子径向部分的本征函数，利用矩阵变量孔恩温德方法，由厄米雅可比多项式构造正交多项式并猜想其为基本带状球函数，还借助多元舒尔多项式获取相关信息及构造函数。

Higher-dimensional Osserman metrics with non-nilpotent Jacobi operators

We exhibit Osserman metrics with non-nilpotent Jacobi operators and with non-trivial Jordan normal form in neutral signature (n,n) for any n which is at least 3. These examples admit a natural almost para-Hermitian structure and are semi para-complex Osserman with non-trivial Jordan normal form as well; they neither satisfy the third Gray identity nor are they integrable.

Harmonic contact metric structures, and submersions

We study harmonic almost contact structures in the context of contact metric manifolds, and an analysis is carried out when such a manifold fibres over an almost Hermitian manifold, as exemplified by the Boothby-Wang fibration. Two types of almost contact metric warped products are also studied, relating their harmonicity to that of the almost Hermitian structure on the base or fibre.

埃尔米特流形的挠率代数与刚性

Torsion algebras of Hermitian manifolds and rigidity

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。

半定Strominger-Bismut-Ricci曲率下紧Hermitian曲面的Kählerness

Kählerness of compact Hermitian surfaces under semi-definite Strominger-Bismut-Ricci curvatures

通过Strominger-Bismut联络的Ricci曲率与挠率的关系以及Chern数恒等式，证明了紧Hermitian曲面在半定Ricci曲率条件下的Kählerness准则。