Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-26T07:33:28.521Z Has data issue: false hasContentIssue false
  • English
  • Français

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
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 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
[2] Chern, S.S., The geometry of G-structures5 Bull. Amer. Math. Soc. 72 (1966), 167–219.Google Scholar
[3] Kobayashi, S., Theory of connections, Ann. Mat. Pura Appl., 43 (1957), 119–194.Google Scholar
[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