Curves in Lorentzian spaces
Nešović, E. ; Petrović-Torgašev, M. ; Verstraelen, L.
Bollettino dell'Unione Matematica Italiana, Tome 8-A (2005), p. 685-696 / Harvested from Biblioteca Digitale Italiana di Matematica
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The notion of ``hyperbolic'' angle between any two time-like directions in the Lorentzian plane L2 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 L2 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 L3 whose natural equations express their curvature and torsion as elementary eigenfunctions of their Laplacian.

La nozione di angolo iperbolico tra due qualsiasi direzioni simili al tempo nel piano di Lorentz L2 è stata appropriatamente definita e studiata da Birman e Nomizu [1, 2]. In questo articolo definiamo la nozione di angolo iperbolico tra due qualsiasi direzioni non nulle in L2 e definiamo una misura sull'insieme di questi angoli iperbolici. Come applicazione, estendiamo il lavoro di Scofield sulle curve euclidee di precessione costante [9] all'ambiente di Lorentz, rendendo così esplicite le curve simili allo spazio in L3 le cui equazioni naturali esprimono la loro curvatura e torsione come autofunzioni elementari del loro Laplaciano.

Publié le : 2005-10-01
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     author = {E. Ne\v sovi\'c and M. Petrovi\'c-Torga\v sev and L. Verstraelen},
     title = {Curves in Lorentzian spaces},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {8-A},
     year = {2005},
     pages = {685-696},
     zbl = {1178.53071},
     mrnumber = {2182423},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2005_8_8B_3_685_0}
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Nešović, E.; Petrović-Torgašev, M.; Verstraelen, L. Curves in Lorentzian spaces. Bollettino dell'Unione Matematica Italiana, Tome 8-A (2005) pp. 685-696. http://gdmltest.u-ga.fr/item/BUMI_2005_8_8B_3_685_0/

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