Affine connections and Gauss-Bonnet theorems in the Heisenberg group

Abstract

In this paper, we compute sub-Riemannian limits of Gaussian curvature associated to two kinds of Schouten-Van Kampen affine connections and the adapted connection for a Euclidean $C^2$-smooth surface in the Heisenberg group away from characteristic points and signed geodesic curvature associated to two kinds of Schouten-Van Kampen affine connections and the adapted connection for Euclidean $C^2$-smooth curves on surfaces. We get Gauss-Bonnet theorems associated to two kinds of Schouten-Van Kampen affine connections in the Heisenberg group.

no. arXiv admin note: substantial text overlap with arXiv:1912.00302

References in corpus (2)

• Rotation surfaces of constant Gaussian curvature as Riemannian approximation scheme in sub-Riemannian Heisenberg space ${\mathbb{H}}^1$
• The Euler Class from a General Connection, Relative to a Metric

Cited by in corpus (1)

• Gauss-Bonnet theorems associated to deformed Schouten-Van Kampen connection in the affine group and the group of rigid motions of the Minkowski plane