标题： 一种绝对平行几何的全局方法 显示英文标题

标题： A Global Approach to Absolute Parallelism Geometry

摘要： 在本文中，我们对可平行化流形（或绝对平行几何）的几何进行了\emph{全局的}的研究，这种几何经常用于应用。 我们从全局观点讨论了不同的线性联络和曲率张量。 我们给出了一个著名线性联络——规范联络的存在性和唯一性定理。 不同的曲率张量仅用规范联络的扭曲张量以紧凑形式表示。 利用Bianchi恒等式，推导出一些有趣的恒等式。 一个重要的四阶特殊张量，我们称之为Wanas张量，被全局定义并进行了研究。 最后，建立了绝对平行空间的基本几何对象的双视角：这些几何对象的表达式在平行化基下计算，并与自然基下的相应局部表达式进行比较。 指出了所考虑的一些几何对象的物理方面。 显示英文摘要

摘要： In this paper we provide a \emph{global} investigation of the geometry of parallelizable manifolds (or absolute parallelism geometry) frequently used for application. We discuss the different linear connections and curvature tensors from a global point of view. We give an existence and uniqueness theorem for a remarkable linear connection, called the canonical connection. Different curvature tensors are expressed in a compact form in terms of the torsion tensor of the canonical connection only. Using the Bianchi identities, some interesting identities are derived. An important special fourth order tensor, which we refer to as Wanas tensor, is globally defined and investigated. Finally a double-view for the fundamental geometric objects of an absolute parallelism space is established: The expressions of these geometric objects are computed in the parallelization basis and are compared with the corresponding local expressions in the natural basis. Physical aspects of some geometric objects considered are pointed out.