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Induced Connections and Imbedded Riemannian Spaces

Published online by Cambridge University Press:  22 January 2016

Shoshichi Kobayashi
Shoshichi Kobayashi*
Affiliation:
University of Washington
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Let P be a principal fibre bundle over M with group G and with projection π : P → M. By definition of a principal fibre bundle, G acts on P on the right. We shall denote this transformation law by ρ

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 10 , June 1956 , pp. 15 - 25
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1956

References

[ 1 ] Chern, S-S., La géométrie des sous-variétés d’un espace euclidien à plusieurs dimensions, Enseignement Math. 40 (1955), 26–46. See also: Topics in differential geometry, Mimeographed notes, Princeton (1951).Google Scholar
[ 2 ] Ehresmann, C., Les connexions infinitésimales dans un espace fibré différentiate, Colloque de Topologie, Bruxelles (1960), 29–55.Google Scholar
[ 3 ] Kobayashi, S., Espaces à connexions affines et riemanniennes symétriques, Nagoya Math. J. 9 (1955), 25–37.Google Scholar
[ 4 ] Kobayashi, S., Holonomy groups of hypersurfaces, this journal.Google Scholar
[ 5 ] Kobayashi, S., Theory of connections I, Mimeographed notes (1955).Google Scholar
[ 6 ] Pontrjagin, L., Some topological invariants of closed Riemannian manifolds, Izvestiya Akad. Nauk SSSR, Ser. Math. 13 (1949), 125–162; Amer. Math. Soc. Trans. No. 49.Google Scholar
[ 7 ] Steenrod, N., Topology of fibre bundles (1951).Google Scholar