Hostname: page-component-6898cfcb55-zsp5v Total loading time: 0 Render date: 2026-11-11T20:34:39.426Z Has data issue: false hasContentIssue false
  • English
  • Français

A Note on Infinitesimal Holonomy Groups*

Published online by Cambridge University Press:  22 January 2016

Albert Nijenhuis
Albert Nijenhuis*
Affiliation:
University of Washington, Seattle, Washington, U.S.A.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

In a recent paper [1], H. Ozeki has extended the author’s results [2] on local and infinitesimal holonomy groups for connections in linear fiber bundles (whose fiber is a vector space) to general fiber bundles whose structure group is a Lie group. Ozeki’s Lemma 7 (corresponding to the author’s Lemma 5.2) appears to be rather crucial in the development, while the proof is somewhat involved.—This note intends to present a more direct proof of the lemma, stating a case in which the local holonomy group H *(x)and the infinitesimal holonomy group H’(x)coincide:

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 12 , December 1957, pp. 145 - 146
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1957

Footnotes

*

Research sponsored by the Office of Naval Research.

References

Literature

[1] Ozeki, H.. Infinitesimal holonomy groups of hundle connections. Nagoya Math. J., 10, 105–123 (1956).CrossRefGoogle Scholar
[2] Nijenhuis, A.. On the holonomy groups of linear connections. Kon. Nederl. Akad. Wetenschappen Amsterdam, Proc, A56 (3), 233–249, A57 (1), 17–25 (=Indag. Math., 15 (3), 233–249; 16 (1), 17–25).Google Scholar