We use a Riemannnian approximation scheme to define a notion of intrinsic Gaussian curvature for a Euclidean C2-smooth surface in the Heisenberg group H away from characteristic points, and a notion of intrinsic signed geodesic curvature for Euclidean C2-smooth curves on surfaces. These results are then used to prove a Heisenberg version of the Gauss–Bonnet theorem. An application to Steiner’s formula for the Carnot–Carathéodory distance in H is provided.

Intrinsic curvature of curves and surfaces and a Gauss–Bonnet theorem in the Heisenberg group

Vecchi E.
2017

Abstract

We use a Riemannnian approximation scheme to define a notion of intrinsic Gaussian curvature for a Euclidean C2-smooth surface in the Heisenberg group H away from characteristic points, and a notion of intrinsic signed geodesic curvature for Euclidean C2-smooth curves on surfaces. These results are then used to prove a Heisenberg version of the Gauss–Bonnet theorem. An application to Steiner’s formula for the Carnot–Carathéodory distance in H is provided.
Gauss–Bonnet theorem; Heisenberg group; Riemannian approximation; Steiner formula; Sub-Riemannian geometry
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11311/1125513
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