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.

Convexity and the finiteness of the number of geodesics. Applications to the multiple-image effect

Masiello, A.;
1999-01-01

Abstract

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/4501
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