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.
Balogh, Z.M., Tyson, J.T., Vecchi, E. (2017). Intrinsic curvature of curves and surfaces and a Gauss–Bonnet theorem in the Heisenberg group. MATHEMATISCHE ZEITSCHRIFT, 287(1-2), 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 (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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
