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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 some types of slant curves in contact pseudo-Hermitian 3-manifolds

Cihan Özgür, Şaban Güvenç (2012)

Annales Polonici Mathematici

We study slant curves in contact Riemannian 3-manifolds with pseudo-Hermitian proper mean curvature vector field and pseudo-Hermitian harmonic mean curvature vector field for the Tanaka-Webster connection in the tangent and normal bundles, respectively. We also study slant curves of pseudo-Hermitian AW(k)-type.

Optimalité systolique infinitésimale de l’oscillateur harmonique

J.C. Álvarez Paiva, Florent Balacheff (2008/2009)

Séminaire de théorie spectrale et géométrie

Nous étudions les aspects infinitésimaux du problème suivant. Soit H un hamiltonien de 2 n dont la surface d’énergie { H = 1 } borde un domaine compact et étoilé de volume identique à celui de la boule unité de 2 n . La surface d’énergie { H = 1 } contient-elle une orbite périodique du système hamiltonien q ˙ = H p p ˙ = - H q dont l’action soit au plus π  ?

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