In this Note, by using a generalization of the classical Fermat principle, we prove the existence and multiplicity of lightlike geodesics joining a point with a timelike curve on a class of Lorentzian manifolds, satisfying a suitable compactness assumption, which is weaker than the globally hyperbolicity.
In questa Nota, usando una generalizzazione del principio di Fermat, si studia l'esistenza e la molteplicità di geodetiche di tipo luce congiungenti un punto con una curva di tipo tempo su una classe di varietà Lorentziane, soddisfacente una condizione di compattezza più debole della globale iperbolicità.
@article{RLIN_1995_9_6_3_155_0,
author = {Fabio Giannoni and Antonio Masiello},
title = {On a variational theory of light rays on Lorentzian manifolds},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
volume = {6},
year = {1995},
pages = {155-159},
zbl = {0848.53041},
mrnumber = {1363784},
language = {en},
url = {http://dml.mathdoc.fr/item/RLIN_1995_9_6_3_155_0}
}
Giannoni, Fabio; Masiello, Antonio. On a variational theory of light rays on Lorentzian manifolds. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 6 (1995) pp. 155-159. http://gdmltest.u-ga.fr/item/RLIN_1995_9_6_3_155_0/
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