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Classification of K-contact forms and spectral invariants of their sub-Laplacians
Eugenio Bellini
A contact form is called K-contact if its Reeb vector field is Killing with respect to some Riemannian metric. In this paper we classify K-contact forms whose Reeb vector field adm…
Curvature measures and the sub-Riemannian Gauss-Bonnet theorem
Davide Barilari, Eugenio Bellini, Andrea Pinamonti
We adopt a measure-theoretic perspective on the Riemannian approximation scheme proving a sub-Riemannian Gauss-Bonnet theorem for surfaces in 3D contact manifolds. We show that the…
Quantitative tightness for three-dimensional contact manifolds: a sub-Riemannian approach
Andrei A. Agrachev, Stefano Baranzini, Eugenio Bellini +1
Through the use of sub-Riemannian metrics we provide quantitative estimates for the maximal tight neighbourhood of a Reeb orbit on a three-dimensional contact manifold. Under appro…
Surfaces of genus in 3D contact sub-Riemannian manifolds
Eugenio Bellini, Ugo Boscain
We consider surfaces embedded in a 3D contact sub-Riemannian manifold and the problem of the finiteness of the induced distance (i.e., the infimum of the length of horizontal curve…
The geometry of Riemannian curvature radii
Eugenio Bellini
In this paper we explore the geometric structures associated with curvature radii of curves with values on a Riemannian manifold . We show the existence of sub-Riemannian m…