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Integrable almost cotangent structures and Legendrian bundles

Published online by Cambridge University Press:  24 October 2008

G. Thompson
G. Thompson
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ont. N2L 3G1, Canada
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Extract

Recently, the present author together with M. Crampin proved a structure theorem for a certain subclass of geometric objects known as almost tangent structures (Crampin and Thompson [8]). As the name suggests, an almost tangent structure is obtained by abstracting one of the tangent bundle's most important geometrical ingredients, namely its canonical 1–1 tensor, and using it to define a certain class of G-structures. Roughly speaking, the structure theorem referred to above may be paraphrased by saying that, if an almost tangent structure is integrable as a G-structure and satisfies some natural global hypotheses, then it is essentially the tangent bundle of some differentiable manifold. (I shall have a further remark to make about the conclusion of that theorem at the end of Section 2.)

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 101 , Issue 1 , January 1987 , pp. 61 - 78
Copyright
Copyright © Cambridge Philosophical Society 1987

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