论文标题
连接和框架束减少
Connections and Frame Bundle Reductions
论文作者
论文摘要
总体而言，重力电势由Levi-Civita连接表示，这是唯一保留该度量的对称连接。在可区分的歧管上，公制用正交结构识别，定义为框架束的洛伦兹的还原。 Levi-Civita连接似乎是保留还原的唯一对称连接。本文将此过程概括为其他引力的侵蚀：Weyl结构，具有Weyl连接，带有Weitzenbock连接的远程处理结构，单模型结构，类似地作为框架束减少出现，并保留了连接。线性组GL的每个亚组H相应减少结构或H结构。它们是框架束的子捆绑包（与GL作为主要组），H作为主要组。歧管M中的线性连接是框架束上的主要连接。给定减少，M上的相应保留连接是保留它的线性连接。我还表明，在3+1形式主义中使用的时间表类似地出现了捆绑夹的结果。
In general relativity, the gravitational potential is represented by the Levi-Civita connection, the only symmetric connection preserving the metric. On a differentiable manifold, a metric identifies with an orthogonal structure, defined as a Lorentz reduction of the frame bundle. The Levi-Civita connection appears as the only symmetric connection preserving the reduction. This paper presents generalization of this process to other aproaches of gravitation: Weyl structure with Weyl connections, teleparallel structures with Weitzenbock connections, unimodular structure, similarly appear as frame bundle reductions, with preserving connections. To each subgroup H of the linear group GL correspond reduced structures, or H-structures. They are subbundles of the frame bundle (with GL as principal group), with H as principal group. A linear connection in a manifold M is a principal connection on the frame bundle. Given a reduction, the corresponding preserving connections on M are the linear connections which preserve it. I also show that the time gauge used in the 3+1 formalism for general relativity similarly appears as the result of a bundle reduction.
