Weitzenbck公式的一点注记

Weitzenbck公式在研究黎曼流形上曲率对调和形式的影响时起了极大的作用;通过导出此公式在局部正交规范标架场中的显式表达式,可以再得到闭的n维正曲率空间形式上的p次微分形式必然为零,其中p=1…n-1。

复流形上的Weitzenböck公式及Gårding不等式

本文主要研究了紧致光滑流形上的向量丛E值p形式的Weitzenböck公式、复流形上的∂-Laplace算子的Weitzenböck恒等式及其应用。先证明Gårding不等式,然后证明了整体理论的Hodge定理。

四面体中著名不等式的统一和加强

本文在证明了Ｐｏｌｙａ－Ｓｚｅｇｏ不等式向四面体推广所得的两种形式等价的同时，统一证明了四面体中的一些著名不等式，并加强了这些不等式。

Classification of Kantowski-Sachs and Bianchi Type Ⅲ Space-Times According to Their Killing Vector Fields in Teleparallel Theory of Gravitation

In this paper we classify Kantowski-Sachs and Bianchi type Ⅲ space-times according to their teleparallel Killing vector fields using direct integration technique. It turns out that the dimension of the telepaxallel Killing vector fields are 4 or 6, which are the same in numbers as in general relativity. In case of 4 the teleparallel Killing vector fields are multiple of the corresponding Killing vector fields in general relativity by some function of t. In the case of 6 Killing vector fields the metric functions become constants and the Killing vector fields in this case are exactly the same as in general relativity. Here we also discuss the Lie algebra in each case.

Detecting Quaternionic Maps Between Hyperkähler Manifolds

For a harmonic map between two hyperkäher manifolds,we prove a Weitzenböck type formula for the defining quantity of quaternionic maps,and apply it to harmonic morphisms.We also provide a sufficient and necessary condition for a smooth map being quaternionic.