4 papers
On the tightness of left-invariant contact structures
Eugenio Bellini
We prove that all left-invariant contact structures on three-dimensional Lie groups are tight. The argument is based on Riemannian methods and establishes a unique factorization pr…
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…
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…
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…