相配群胚上的诱导联络

本文引入了相配群胚和相配主丛的概念,它们是一对具有相同传递函数的局部平凡李群胚（Г→_→P,α,β）和主丛（B,P,π,G）.我们首先考察了相配群胚Г的内子群胚GГ的局部平凡化,利用这个局部平凡化证明了在B和GГ之间自然存在着一个丛同构.通过这个丛同构以及B的联络日逐步得到了H在GГ和Г上的诱导联络,进而定义了Г上分别以α,β为投影的左联络和右联络,这两个联络都是在Г上整体有定义的,与以往李群胚上的联络只是定义在李代数胚上不同.

Induced Connections of Associated Groupoids

In this paper,the new concepts of associated groupoids and associated principal bundle be introduced which are a pair of a locally trivial Lie groupoids(F (→→)P,α,β)and a principal bundle(B,P,π,G)with the same transition function.At first,the locally trivializations of the inner subgroupoids GF of F is considered,then,by using the locally trivializations,it is proved that there is a natural bundle isomorphism between B and GF.By this bundle isomorphism and the connections H of B.the induced connections on GГ and Г are obtained gradually.Furthermore,we constructed a left connections and a right connections of Г which are respectively regard α,β as their projections.The two connections are defined on the whole Г.It is differs from before that the connections of a Lie groupoids only be defined on its Lie algebroids.