论文标题
无限同质性和捆绑包
Infinitesimal homogeneity and bundles
论文作者
论文摘要
令$ q \ to m $为$ g $ undle，$ b_0 $ a $ q $。我们在相关的矢量束$ q \ times_gv $相对于$ b_0 $的相关载体捆绑包中引入了无限的同质性条件，并受到众所周知的Ambrose-Serger定理的启发，我们证明存在满足平行性条件系统的连接。我们解释了如何使用该通用定理来通过适当的选择数据系统来证明已知的Ambrose-Singer类型定理。我们还获得了新的应用程序，这些应用程序无法使用已知的形式主义，例如局部均匀旋转器的分类定理。 最后，我们介绍了三倍的$（g，p \ stackrel {p} {\ to} m，a）$的自然本地同质性和本地对称条件，该条件由$ m $上的riemannian度量，$ m $的主要捆绑包，以及$ p $的连接。我们的主要结果涉及本地均质和局部对称的三元组，并且可以将其视为Ambrose-Singer和Cartan定理的捆绑版本。
Let $Q\to M$ be a principal $G$-bundle, and $B_0$ a connection on $Q$. We introduce an infinitesimal homogeneity condition for sections in an associated vector bundle $Q\times_GV$ with respect to $B_0$, and, inspired by the well known Ambrose-Singer theorem, we prove the existence of a connection which satisfies a system of parallelism conditions. We explain how this general theorem can be used to prove the known Ambrose-Singer type theorems by an appropriate choice of the initial system of data.We also obtain new applications, which cannot be obtained using the known formalisms, e.g. a classification theorem for locally homogeneous spinors. Finally we introduce natural local homogeneity and local symmetry conditions for triples $(g,P\stackrel{p}{\to} M,A)$ consisting of a Riemannian metric on $M$, a principal bundle on $M$, and a connection on $P$. Our main results concern locally homogeneous and locally symmetric triples, and they can be viewed as bundle versions of the Ambrose-Singer and Cartan theorem.
