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Prolongations of Connections to Tangential Fibre Bundles of Higher Order

Published online by Cambridge University Press:  22 January 2016

Akihiko Morimoto
Akihiko Morimoto*
Affiliation:
Nagoya University
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In the previous paper [3] we have studied the prolongations of G-structures to tangent bundles of higher order. The purpose of the present paper is to study the prolongations of connections to tangential fibre bundles of higher order, and to generalize the results due to S. Kobayashi [1] for the case of usual tangent bundle —— in fact, the arguments in [1] will be, in a sense, more or less simplified and clarified by using the notion of tangent bundles of higher order. In addition, as a consequence of our results, we shall obtain the prolongations of linear (affine) connections to tangent bundles of higher order.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 40 , December 1970 , pp. 85 - 97
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1970

References

[1] Kobayashi, S., Theory of connections, Ann. Mat. Pura Appl., 43(1957), 119–194.CrossRefGoogle Scholar
[2] Morimoto, A., Prolongations of G-structures to tangent buncles, Nagoya Math. J. 32 (1968), 67–108.CrossRefGoogle Scholar
[3] Morimoto, A., Prolongations of G-structures to tangent bundles of higher order, Nagoya Math. J. 38(1970), 153–179.Google Scholar