We describe a canonical extension of the sub-Riemannian metric and study geometric properties of the obtained Riemannian manifold

Teichm¨ uller space, group of diffeomorphisms, Lie-Fr´echet group, Virasoro-Bott group, Virasoro algebra, sub-Riemannian geometry, Euler-Arnold equation , geodesic, K¨ahlerian

Sub-Riemannian Geometry is proved to play an important role in many applications, e.g., Mathematical Physics and Control Theory. The simplest example of sub-Riemannian structure

Based on the Löwner–Kufarev parametric representation we get a partially integrable Hamiltonian system in which the first integrals are Kirillov’s operators for a representation of

2.4 Intrinsic rolling of manifolds 21 The fact that the kinematic constraints of no-slipping and no-twisting can be under- stood as a distribution of rank n over the

The geodesics in the sub-Riemannian manifolds are defined as a projection of the solution to the corresponding Hamiltonian system onto the manifold.. It is a good generalization of

Namely, we describe the sub-Riemannian geometry

The main difference between the sub-Riemannian manifold and Riemannian one is the presence of a smooth subbundle of the tangent bundle, generating the entire tangent bundle by means

More specifically, we study the sub-Riemannian geometry arising from the contact distribution for the spheres S 2n + 1 with metric given as a restriction of the usual Riemannian