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Skew connections in vector bundles and their prolongations

Published online by Cambridge University Press:  09 April 2009

Juraj Virsik
Juraj Virsik
Affiliation:
Monash University
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The paper is closely related to [1] and [2]. A skew connection in a vector bundle E as defined here is a pseudo-connection (in the sense of [1]) which can be changed into a connection by transforming separately the bundle E itself and the bundle of its differentials, i.e. one-forms on the base with values in E. The properties of skew connections are thus expected to be only “algebraically” more complicated than those of connections; especially one can follow the pattern of [1], and prolong them to obtain higher order semi-holonomic and non-holonomic pseudo-connections. It is shown in this paper that under some circumstances the main theorem of [1] or [2] applies also to skew connections.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 13 , Issue 3 , May 1972 , pp. 343 - 353
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Virsik, J., Non-holonomic connections on vector bundles, Czech. Math. J. 17 (1967), I: 108–147; II: 200–224.CrossRefGoogle Scholar
[2]Virsik, J., Über Zusammenhänge höherer Ordnungen in Vektorraumbündeln, Math. Nachrichten 34 (1967), 219–227.Google Scholar
[3]Feldmann, E., The geometry of immersions, Bull. Amer. Math. Soc. 69 (1963), 693–698.Google Scholar
[4]Libermann, P., Sur la géométrie des prolongements des espaces fibrés vectoriels, Ann. Inst. Fourier, Grenoble 14 (1964), 145–172.Google Scholar
[5]Pohl, W., Connections in differential geometry of higher order, Tranzactions Amer. Math. Soc. 125 (1966), 310–325.Google Scholar
[6]Que, N., Du prolongement des espaces fibrés et des structures infinitésimales, Ann. Inst. Fourier, Grenoble 17 (1967), 157–223.Google Scholar