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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 geometry of curves of flags of constant type

Boris Doubrov, Igor Zelenko (2012)

Open Mathematics

We develop an algebraic version of Cartan’s method of equivalence or an analog of Tanaka prolongation for the (extrinsic) geometry of curves of flags of a vector space W with respect to the action of a subgroup G of GL(W). Under some natural assumptions on the subgroup G and on the flags, one can pass from the filtered objects to the corresponding graded objects and describe the construction of canonical bundles of moving frames for these curves in the language of pure linear algebra. The scope...

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