Curves in Lorentzian spaces
Bollettino della Unione matematica italiana, Série 8, 8B (2005) no. 3, pp. 685-696
Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica
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.
@article{BUMI_2005_8_8B_3_a9,
author = {Ne\v{s}ovi\'c, E. and Petrovi\'c-Torga\v{s}ev, M. and Verstraelen, L.},
title = {Curves in {Lorentzian} spaces},
journal = {Bollettino della Unione matematica italiana},
pages = {685--696},
publisher = {mathdoc},
volume = {Ser. 8, 8B},
number = {3},
year = {2005},
zbl = {1178.53071},
mrnumber = {MR2182423},
language = {en},
url = {http://geodesic.mathdoc.fr/item/BUMI_2005_8_8B_3_a9/}
}
TY - JOUR AU - Nešović, E. AU - Petrović-Torgašev, M. AU - Verstraelen, L. TI - Curves in Lorentzian spaces JO - Bollettino della Unione matematica italiana PY - 2005 SP - 685 EP - 696 VL - 8B IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/BUMI_2005_8_8B_3_a9/ LA - en ID - BUMI_2005_8_8B_3_a9 ER -
Nešović, E.; Petrović-Torgašev, M.; Verstraelen, L. Curves in Lorentzian spaces. Bollettino della Unione matematica italiana, Série 8, 8B (2005) no. 3, pp. 685-696. http://geodesic.mathdoc.fr/item/BUMI_2005_8_8B_3_a9/