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

Balogh, Zoltan; Tyson, Jeremy; Vecchi, Eugenio (2017). Intrinsic curvature of curves and surfaces and a Gauss-Bonnet theorem in the Heisenberg group. Mathematische Zeitschrift, 287(1-2), pp. 1-38. Springer 10.1007/s00209-016-1815-6

[img]
Preview
Text
10.1007_s00209-016-1815-6.pdf - Published Version
Available under License Publisher holds Copyright.

Download (715kB) | Preview

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.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Balogh, Zoltan, Tyson, Jeremy, Vecchi, Eugenio

Subjects:

500 Science > 510 Mathematics

ISSN:

0025-5874

Publisher:

Springer

Language:

English

Submitter:

Olivier Bernard Mila

Date Deposited:

17 Apr 2018 09:49

Last Modified:

05 Dec 2022 15:09

Publisher DOI:

10.1007/s00209-016-1815-6

Related URLs:

BORIS DOI:

10.7892/boris.109136

URI:

https://boris.unibe.ch/id/eprint/109136

Actions (login required)

Edit item Edit item
Provide Feedback