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Integrable spreads and spaces of constant curvature

Published online by Cambridge University Press:  14 November 2011

H. R. Farran  and
S. A. Robertson
H. R. Farran
Affiliation:
Department of Mathematics, Kuwait University, P.O. Box 5969, 13060 Safat, Kuwait
S. A. Robertson
Affiliation:
Department of Mathematics, University of Southampton, Southampton SO9 5NH, U.K.
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Synopsis

This paper is a continuation of [2], where we introduced the notion of global k-spreads on manifolds. Here we show that the space of all k-spreads on a manifold has the structure of an affine space, modelled on the vector space of sections of a certain vector bundle. We give some sufficient conditions for a manifold admitting an integrable k-spread to be a space of constant curvature and answer one of the questions raised in [2].

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 109 , Issue 3-4 , 1988 , pp. 225 - 229
Copyright
Copyright © Royal Society of Edinburgh 1988

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References

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