Mechanics Systems on Para-Kaehlerian Manifolds of Constant J-Sectional Curvature

Anti-Kaehlerian Manifolds

An anti-Kaehlerian manifold is a complex manifold with an anti-Hermitian metric and a parallel almost complex structure. It is shown that a metric on such a manifold must be the real part of a holomorphic metric. It is proved that all odd Chern numbers of an anti-Kaehlerian manifold vanish and that complex parallelisable manifolds (in particular the factor space G/D of a complex Lie group G over the discrete subgroup D) are anti-Kaehlerian manifolds. A method of generating new solutions of Einstein equations by using the theory of anti-Kaehlerian manifolds is presented.

Constrained Paracomplex Mechanical Systems

In this study, it is introduced paracomplex analogue of Lagrangians and Hamiltonians with constraints in the framework of para-Kaehlerian manifolds. The geometrical and mechanical results on the constrained mechanical system have also been discussed.

从流体动力学中的反比关系出发研究密度流形的几何计算

Geometric calculations on density manifolds from reciprocal relations in hydrodynamics

本文通过研究流体动力学密度流形上的几何计算，推导了黎曼度和截面曲率，并展示了零范围模型的曲率特性。

Examples of Self-dual, Einstein metrics of $(2,2)$-signature

In this paper we construct a family of examples of self-dual Einstain metrics of neutral signature, which are not Ricci flat, nor locally homogenous. Curvature of these manifolds is studied in details. These are obtained by the para-quaternionic reduction. We compare our examples with the orbifolds $\oo$ given by Galicki and Lawson, for which some new properties are also established. Particularly, the sign and the pinching of their sectional curvatures are studied.

从主方程中的互易关系出发的概率流形几何计算

Geometric calculations on probability manifolds from reciprocal relations in Master equations

本文从主方程互易关系出发，研究概率流形的几何计算，推导了Levi-Civita连接、梯度等算子，并给出了两个具体例子。