Gauss-Bonnet theorems and the Lorentzian Heisenberg group

Authors

Tong Wu
SINING WEI
YONG WANG

DOI

10.3906/mat-2011-19

Abstract

In this paper, we compute sub-Riemannian limits of Gaussian curvature for a C$^{2}$-smooth surface in the Lorentzian Heisenberg group for the second Lorentzian metric and the third Lorentzian metric and signed geodesic curvature for C$^{2}$-smooth curves on surfaces. We get Gauss-Bonnet theorems in the Lorentzian Heisenberg group for the second Lorentzian metric and the third Lorentzian metric.

Keywords

Lorentzian Heisenberg group, the second Lorentzian metric, the third Lorentzian metric, Gauss-Bonnet theorem, sub-Riemannian limit

First Page

718

Last Page

741

Recommended Citation

Wu, Tong; WEI, SINING; and WANG, YONG (2021) "Gauss-Bonnet theorems and the Lorentzian Heisenberg group," Turkish Journal of Mathematics: Vol. 45: No. 2, Article 7. https://doi.org/10.3906/mat-2011-19
Available at: https://journals.tubitak.gov.tr/math/vol45/iss2/7