Gauss-Bonnet formula for general Lorentzian surfaces
The author establishes a new Gauss-Bonnet formula on general Lorentzian surfaces, which is formally very like the classical one. The length of a curve and the angle in Riemannian manifolds are replaced by the Lorentzian length and the sectional measure respectively. By the new Gauss-Bonnet formula the author derives some global properties on Lorentzian surfaces, which are original either in results or in techniques. In addition, the dual theorem of Jacobi on the de Sitter space \(S^ 2\!_ 1\) in the 3-dimensional flat Lorentzian space \(L^ 3\) is given.
scientific article; zbMATH DE number 3850043