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On contact p -spheres

Mathias Zessin (2005)

Annales de l’institut Fourier

We study invariant contact p -spheres on principal circle-bundles and solve the corresponding existence problem in dimension 3. Moreover, we show that contact p - spheres can only exist on ( 4 n - 1 ) -dimensional manifolds and we construct examples of contact p -spheres on such manifolds. We also consider relations between tautness and roundness, a regularity property concerning the Reeb vector fields of the contact forms in a contact p -sphere.

On cotangent bundles of some natural bundles

Kolář, Ivan (1994)

Proceedings of the Winter School "Geometry and Physics"

The author studies relations between the following two types of natural operators: 1. Natural operators transforming vector fields on manifolds into vector fields on a natural bundle F ; 2. Natural operators transforming vector fields on manifolds into functions on the cotangent bundle of F . It is deduced that under certain assumptions on F , all natural operators of the second type can be constructed through those of the first one.

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