Curves in Lorentzian spaces

Nešović, E. ; Petrović-Torgašev, M. ; Verstraelen, L.

Bollettino della Unione matematica italiana, Série 8, 8B (2005) no. 3, pp. 685-696

Résumé

The notion of ``hyperbolic'' angle between any two time-like directions in the Lorentzian plane $L^{2}$ was properly defined and studied by Birman and Nomizu [1,2]. In this article, we define the notion of hyperbolic angle between any two non-null directions in $L^{2}$ and we define a measure on the set of these hyperbolic angles. As an application, we extend Scofield's work on the Euclidean curves of constant precession [9] to the Lorentzian setting, thus expliciting space-like curves in $L^{3}$ whose natural equations express their curvature and torsion as elementary eigenfunctions of their Laplacian.