Sub-Riemannian curvature and a Gauss-Bonnet theorem in the Heisenberg group

Zoltán Balogh, Jeremy T. Tyson, Eugenio Vecchi

We use a Riemannnian approximation scheme to define a notion of $\text{sub-Riemannian Gaussian curvature}$ for a Euclidean $C^2$-smooth surface in the Heisenberg group $\mathbb…