Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-26T05:48:46.321Z Has data issue: false hasContentIssue false
  • English
  • Français

Prolongations of linear connections to the frame bundle

Published online by Cambridge University Press:  17 April 2009

Luis A. Cordero  and
Manuel de Leon
Luis A. Cordero
Affiliation:
Departamento de Geometria y Topologia, Facultad de Matematicas, Universidad de Santiago de Compostela, Spain.
Manuel de Leon
Affiliation:
Departamento de Geometria y Topologia, Facultad de Matematicas, Universidad de Santiago de Compostela, Spain.
Rights & Permissions [Opens in a new window]

Abstract

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 this paper we construct the prolongation of a linear connection Γ on a manifold Μ to the bundle space of its frame bundle, and show that such prolongated connection coincides with the so-called complete lift of Γ to .

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 28 , Issue 3 , December 1983 , pp. 367 - 381
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Cordero, Luis A. and Leon, Manuel de, “Lifts of tensor fields to the frame bundle”, Rend. Cir. Mat. Palermo (to appear).Google Scholar
[2]Cordero, Luis A. and Leon, Manuel de, “Prolongations of G-structures to the frame bundle”, submitted.Google Scholar
[3]Kobayashi, S., “Theory of connections”, Ann. Mat. Pura Appl. 43 (1957), 119–194.CrossRefGoogle Scholar
[4]Kobayashi, S. and Nomizu, K., Foundations of differential geometry, Vol. I (Interscience, New York, 1963).Google Scholar
[5]Mok, K.P., “Complete lifts of tensor fields and connections to the frame bundle”, Proc. London Math. Soc. (2) 32 (1979), 72–88.CrossRefGoogle Scholar
[6]Morimoto, A., “Prolongation of geometric structures” (Mathematical Institut, Nagoya University, Japan, 1969).Google Scholar
[7]Morimoto, A., “Prolongation of connections to tangential fibre bundles of higher order”, Nagoya Math. J. 40 (1970), 85–97.CrossRefGoogle Scholar