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

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

Mar 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999cqgra..16..731g&link_type=abstract

Classical and Quantum Gravity, Volume 16, Issue 3, pp. 731-748 (1999).

Mathematics

9

Scientific paper

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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