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Integrable spreads

Published online by Cambridge University Press:  14 November 2011

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

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
Copyright
Copyright © Royal Society of Edinburgh 1984

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