Periodic geodesics for contact sub-Riemannian 3D manifolds

Yves Colin de Verdìère (1)

1 IF - Institut Fourier

The goal of this paper is to study periodic geodesics for sub-Riemannian metrics on a contact 3D-manifold. We develop two rather independent subjects: 1) The existence of closed geodesics spiraling around periodic Reeb orbits for a generic metric. 2) The precise study of the periodic geodesics for a right invariant metric on a quotient of SL2(R)

Mots clés: sub-Riemannian geometry; periodic geodesics; Euler equation

Domaines: Géométrie différentielle [math.DG]; Systèmes dynamiques [math.DS]; Géométrie symplectique [math.SG]; Théorie spectrale [math.SP]; Optimisation et contrôle [math.OC]

Yves Colin de Verdìère. Periodic geodesics for contact sub-Riemannian 3D manifolds. 2022. ⟨hal-03589895⟩