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 / Balogh, Zoltan M.; Tyson, Jeremy T.; Vecchi, Eugenio. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - 287:1-2(2017), pp. 1-38. [10.1007/s00209-016-1815-6]
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 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.| File | Dimensione | Formato | |
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Balogh_Intrinsic_2017.pdf
Open Access dal 28/11/2019
Note: https://link.springer.com/article/10.1007/s00209-016-1815-6
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