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Integrable spreads

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, Kuwait
S. A. Robertson
Affiliation:
Faculty of Mathematical Studies, University of Southampton. Southampton SO9 5NH
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Synopsis

For any integer k such that 0≦k≦m, Mk denotes the Grassmann bundle of tangent k-planes on the m-manifold M. A k-spread on M is a field Φ of tangent k-planes on Mk such that the derivative of the projection maps Φ(λ) to λ. Previous work by Douglas and others studied the local properties of such spreads. Here we develop the global theory, with special emphasis on the case in which Φ is integrable.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 96 , Issue 3-4 , 1984 , pp. 206 - 210
Copyright
Copyright © Royal Society of Edinburgh 1984

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References

1Cartan, E.. Legons sur les Espaces de Riemann (Paris: Hermann, 1928).Google Scholar
2Clark, R. S.. Projective collineations in a space of K-spreads. Proc. Cambridge Philos. Soc. 41 (1945), 210–223.CrossRefGoogle Scholar
3Davies, E. T.. On the isomorphic transformations of a space of K-spreads. J. London Math. Soc. 18 (1943), 100–107.CrossRefGoogle Scholar
4Douglas, J.. The general geometry of paths. Ann. of Math. 29 (1928), 143–168.CrossRefGoogle Scholar
5Douglas, J.. Systems of K-dimensional manifolds in an N-dimensional space. Ann. of Math. 105 (1931), 707–733.CrossRefGoogle Scholar
6Veblen, O. and Thomas, T. Y.. The geometry of paths. Trans. Amer. Math. Soc. 25 (1923), 551–608.CrossRefGoogle Scholar
7Wang, H. C.. Path manifolds in a general space of paths. J. London Math. Soc. 21 (1946), 134–139.CrossRefGoogle Scholar
8Wang, H. C.. Axiom of the plane in a general space of paths. Ann. of Math. 49 (1948), 731–737.CrossRefGoogle Scholar