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Sur les toupies et les p-sphères de contact

Abstract : My thesis is a study of contact circles and more generally of contact p-spheres from a topological, a geometrical and an algebraic point of view. A contact p-sphere is the set of normalizes linear combinations of p+1 contact forms if all these forms are contact.
In the first part we consider invariant contact p-spheres on principal circle-bundles. We classify 3-dimensional principal circle-bundles on which invariant p-spheres exist and we construct examples.
In the geometrical part we study the set of contact structures which are associated to the elements of a contact circle. We introduce contact sheaves and contact tops (on Riemannian manifolds). We classify the manifolds on which contact tops exist and we characterize the metrics for which there might exist contact tops on a given manifold.
In the algebraic part we analyse Lie groups of dimensions 3 and 7 with left-invariant contact p-spheres. We get classification theorems and construct examples.
We also prove that there are no contact p-spheres on (4n+1)-dimensional manifolds (for p 1) and that on any (4n-1)-spheres there is a contact ( (4n)-1)-sphere, where is the Adams number.
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Contributor : Mathias Zessin <>
Submitted on : Saturday, February 12, 2005 - 9:16:06 AM
Last modification on : Tuesday, October 16, 2018 - 2:26:02 PM
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  • HAL Id : tel-00008469, version 1



Mathias Zessin. Sur les toupies et les p-sphères de contact. Mathématiques [math]. Université de Haute Alsace - Mulhouse, 2004. Français. ⟨tel-00008469⟩



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