变形原理与几何、物理中的平行问题
Deformation principle and problem of parallelism in geometry and physics
摘要：
变形原理允许人们得到一个非常广泛的一类非均匀几何作为变形的结果正常欧几里德几何。黎曼几何也是通过欧几里得几何的变形而得到的。变形原理的应用似乎是不连续的，黎曼几何似乎不完全一致。研究并比较了两个向量并行性的两种不同定义。第一个定义是基于变形原理。第二个定义是黎曼几何中常用的平行性定义。它表明，第二个定义是不一致的。它导致了黎曼几何中绝对平行性的缺失以及在描述时空几何时对黎曼几何框架外的结果的歧视。
英文摘要：
The deformation principle admits one to obtain a very broad class of nonuniform geometries as a result of deformation of the proper Euclidean geometry. The Riemannian geometry is also obtained by means of a deformation of the Euclidean geometry. Application of the deformation principle appears to be not consecutive, and the Riemannian geometry appears to be not completely consistent. Two different definitions of two vectors parallelism are investigated and compared. The first definitions is based on the deformation principle. The second definition is the conventional definition of parallelism, which is used in the Riemannian geometry. It is shown, that the second definition is inconsistent. It leads to absence of absolute parallelism in Riemannian geometry and to discrimination of outcome outside the framework of the Riemannian geometry at description of the space-time geometry.
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