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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

1Cartan, É.. Leçons sur La Géométrie des éspaces de Riemann (Paris: Gauthier-Villars, 1946).Google Scholar
2Farran, H. R. and Robertson, S. A.. Integrable Spreads. Proc. Roy. Soc. Edinburgh Seel A. 96 (1984), 206–210.CrossRefGoogle Scholar
3Kobayashi, S. and Nomizu, K.. Foundations of Differential Geometry, Vol. I (New York: Interscience, 1963).Google Scholar
4Leung, D. S. and Nomizu, K.. The axiom of spheres in Riemannian Geometry. J. Differential Geometry 5 (1971), 487–489.CrossRefGoogle Scholar
5Spivak, M.. A Comprehensive Introduction to Differential Geometry Vol. 4 (Boston: Publish or Perish, 1975).Google Scholar