We discuss the relations between the notion of convexity in a Riemannian framework and finiteness of the number of geodesics between two fixed points. The results obtained can be applied to the study of lightlike geodesics joining a point and a timelike curve in a conformally static Lorentzian manifold. These geodesics are interpreted as light rays between a light source and an event of a relativistic spacetime; thus our results may be used for a mathematical description of the gravitational lensing effect.
|Titolo:||Convexity and the finiteness of the number of geodesics. Applications to the multiple-image effect|
|Data di pubblicazione:||1999|
|Digital Object Identifier (DOI):||10.1088/0264-9381/16/3/008|
|Appare nelle tipologie:||1.1 Articolo in rivista|