Gauss-Bonnet theorem in Lorentzian Sasakian space forms

Abstract

In this paper, we use a Lorentzian approximation scheme to compute the sub-Lorentzian limit of curvatures for curves and Lorentzian surfaces in the Lorentzian Bianci-Cartan-Vranceanu model of 3-dimensional Lorentzian Sasakian space forms. Based on these results, we get a Gauss-Bonnet theorem in the Lorentzian Sasakian space forms.

Keywords

• lorentzian sasakian space forms
• gauss-bonnet theorem
• lorentzian approximation scheme
• sub-riemannian geometry
• curvature