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Prolongations of G-Structures to Tangent 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 [4] we have studied the prolongations of G-structures to tangent bundles. The purpose of the present paper is to generalize the previous prolongations and to look at them from a wide view as a special case by considering the tangent bundles of higher order. In fact, in some places, the arguments and calculations in [4] are more or less simplified. Since the usual tangent bundle T(M) of a manifold M considers only the first derivatives or first contact elements of M, the previous paper contains, in most parts, only the calculation of derivatives of first order.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 38 , March 1970 , pp. 153 - 179
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1970

References

[1] Bernard, D., Sur la géometrie différentielle des G-structures, Ann. Inst. Fourier 10 (1960), 151–270.Google Scholar
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[4] Morimoto, A., Prolongations of G-structures to tangent bundles, Nagoya Math. J. 32 (1968), 67–108.Google Scholar
[5] Steenrod, N., The topology of fibre bundles, Princeton Univ. Press 1951.CrossRefGoogle Scholar
[6] Sternberg, S., Lectures on Differential Geometry, Englewood Cliffs 1964.Google Scholar
[7] Ishihara, K. Yano-S., Differential geometry of tangent bundles of order 2, to appear.Google Scholar