论文标题
用于一般均质歧管的Ambrose-Singer定理，并应用于符号几何形状
The Ambrose-Singer Theorem for general homogeneous manifolds with applications to symplectic geometry
论文作者
论文摘要
本文的主要结果提供了配备某些几何结构（不一定是伪里曼尼亚语）的还原均匀空间的表征，就某些连接的存在而言。结果概括了Riemannian同质空间的Ambrose和歌手的众所周知的结果，以及其对文献中其他几何形状的扩展。歧管必须连接并简单地连接，连接必须完整，并且必须满足一组几何部分微分方程。如果连接不完整或不简单地连接歧管，则结果提供了还原性局部均匀歧管的表征。最后，我们在本地框架中使用这些结果与显式表达式进行分类，还要还原局部均匀的几乎符合性，符号和联邦歧管。
The main result of this article provides a characterization of reductive homogeneous spaces equipped with some geometric structure (non necessarily pseudo-Riemannian) in terms of the existence of certain connection. The result generalizes the well-known result of Ambrose and Singer for Riemannian homogeneous spaces, as well as its extensions for other geometries found in the literature. The manifold must be connected and simply connected, the connection has to be complete and has to satisfy a set of geometric partial differential equations. If the connection is not complete or the manifold is not simply-connected, the result provides a characterization of reductive locally homogeneous manifolds. Finally, we use these results in the local framework to classify with explicit expressions reductive locally homogeneous almost symplectic, symplectic and Fedosov manifolds.
