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Infinitesimal Holonomy Groups of Bundle Connections

Published online by Cambridge University Press:  22 January 2016

Hideki Ozeki
Hideki Ozeki*
Affiliation:
Mathematical Institute Nagoya University
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In Introduction In differential geometry of linear connections, A. Nijenhuis has introduced the concepts of local holonomy group and infinitesimal holonomy group and obtained many interesting results [6].

The purpose of the present note is to generalize his results to the case of connections in arbitrary principal fiber bundles with Lie structure groups. The concept of local holonomy group can be immediately generalized and has been already utilized by S. Kobayashi [4]. Our main results are Theorems 4 and 5 on infinitesimal holonomy groups. The proofs depend on a little sharpened form of a theorem of Ambrose-Singer [1]. In the case of linear connections, our infinitesimal holonomy group coincides with that of Nijenhuis, as we shall show in Section 6.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 10 , June 1956 , pp. 105 - 123
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1956

References

Bibliographie

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