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.

中文翻译：

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无穷小的同质性和束

令 $Q\to M$ 是一个主体 $G$-bundle，$B_0$ 是 $Q$ 上的一个连接。我们为关联向量丛 $Q\times_GV$ 中的部分引入关于 $B_0$ 的无穷小同质性条件，并且受众所周知的 Ambrose-Singer 定理的启发，我们证明了满足并行系统的连接的存在使适应。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, eg a classification theorem for locally同质旋量。最后，我们介绍了三元组 $(g,P\stackrel{p}{\to} M,A)$ 的自然局部同质性和局部对称条件，包括 $M$ 上的黎曼度量，$M$ 上的主丛，和 $P$ 上的连接。我们的主要结果涉及局部齐次和局部对称的三元组，它们可以被视为 Ambrose-Singer 和 Cartan 定理的捆绑版本。