Geodesic completeness for some meromorphic metrics

Details Geodesic completeness for some meromorphic metrics Geodesic completeness for some meromorphic metrics

2002-04-04

arxiv.org/abs/math/0204061v1

Paru sur Rivista di matematica dell'universit\a di Parma, 4/2001

Mathematics

Complex Variables

C'est un r\'esum\'e de "Geodesic completeness for meromorphic metrics: the case of coercive ones" de l'auteur; LaTeX; 20 pages

Scientific paper

In this paper we investigate possible extensions of the idea of geodesic completeness in complex manifolds, following two directions: metrics are somewhere allowed not to be of maximum rank, or to have 'poles' somewhere else. Geodesics are eventually defined on Riemann surfaces over regions in the Riemann sphere. Completeness theorems are given in the framework of warped products of Riemann surfaces.

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