论射影结构的结构形式

A. Kuleshov
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引用次数: 0

摘要

光滑流形上的射影结构是一个极大集,使得它的所有过渡映射都是分数阶线性变换。我们的目的是用高阶框架束和它们的结构形式来解释这个概念。结果表明,投影结构生成微分几何结构序列。步骤1。对于光滑流形,构造了与流形上的二阶系束相关联的商系束。步骤2。给定流形上的射影结构,构造了商框架束到高阶框架束的映射。这些映射就是微分几何结构。步骤3。考虑了通过映射的框架束结构形式的回调。这些被称为射影结构的结构形式。它们的外在微分用形式本身来表示。这些表达式与射影空间的结构方程一致。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the structure forms of a projective structure
A projective structure on a smooth manifold is a maximal atlas such that all its transition maps are the fractional linear transformations. Our aim is to interpret this notion in terms of the higher order frame bundles and their structure forms. It is shown that the projective structure gener­ates the sequence of differential geometric structures. The construction is following: Step 1. For a smooth manifold the so-called quotient frame bundle as­sociated to the 2nd order frame bundle on the manifold is constructed. Step 2. Given projective structure on the manifold, the mappings from the quotient frame bundle to the higher order frame bundles are con­structed. These mappings are the differential geometric structures. Step 3. The pullbacks of the structure forms of the frame bundles via the mappings are considered. These are called structure forms of the pro­jective structure. The expressions of their exterior differentials in terms of the forms themselves are found. These expressions coincide with the structure equations of a projective space.
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