We use a Riemannnian approximation scheme to define a notion of intrinsic Gaussian curvature for a Euclidean (Formula presented.)-smooth surface in the Heisenberg group (Formula presented.) away from characteristic points, and a notion of intrinsic signed geodesic curvature for Euclidean (Formula presented.)-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 (Formula presented.) is provided.
Intrinsic curvature of curves and surfaces and a Gauss–Bonnet theorem in the Heisenberg group
VECCHI, EUGENIO
2017
Abstract
We use a Riemannnian approximation scheme to define a notion of intrinsic Gaussian curvature for a Euclidean (Formula presented.)-smooth surface in the Heisenberg group (Formula presented.) away from characteristic points, and a notion of intrinsic signed geodesic curvature for Euclidean (Formula presented.)-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 (Formula presented.) is provided.File in questo prodotto:
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