La metrique infinitesimale de Kobayashi et la caracterisation des domaines convexes bornes

摘要

This paper deals with the characterization of a domain D in C~n by the Kobayashi infinitesimal metric in a neighborhood of a point a of D. I prove this characterization in the following cases: a domain D in C analytically isomorphic to the open unit disc, an hyperbolic domain D in D, a bounded strictly convex domain D in C~n and also a bounded convex domain D in C~n which is isomorphic to an open unit ball. The proofs use the result of L. Lempert on the equality of the Caratheodory and Kobayashi infinitesimal metric on convex domains and the notion of complex geodesic.