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Liftings of Tensor Fields and Connections 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 papers [1], [2] we have studied the prolongations of G-structures to tangent bundles of arbitrary order, and in [3] we have considered the prolongations of connections to the tangential fibre bundles of higher order. The purpose of the present paper is to study the liftings of tensor fields and affine connections to tangent bundles of higher order. In fact, most of results in [4], [5] will be generalized in a natural fashion and some of the formulas concerning vertical and complete lifts in [5] will be unified and generalized in our formulas concerning ‹Λ›-lifts (cf. §3).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 40 , December 1970 , pp. 99 - 120
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1970

References

[1] Morimoto, A., Prolongations of G-structures to tangent bundles, Nagoya Math. J., 32 (1968), 67–108.Google Scholar
[2] Morimoto, A., Prolongations of G-structures to tangent bundles of higher order, Nagoya Math. J. 38(1970), 153–179.Google Scholar
[3] Morimoto, A., Prolongations of connections to tangential fibre buncles of higher order, to appear.Google Scholar
[4] Yano, K. and Ishihara, S., Differential geometry of tangent bundles of order 2, to appear.Google Scholar
[5] Yano, K. and Kobayashi, S., Prolongations of tensor fields and conncetions to tangent bundles I, J. Math. Soc. Japan, 18(1966), 194–210.Google Scholar