We shall prove a Poincaré–Bendixson theorem describing the asymptotic behavior of geodesics for a meromorphic connection on a compact Riemann surface. We shall also briefly discuss the case of non-compact Riemann surfaces, and study in detail the geodesics for a holomorphic connection on a complex torus.

A Poincaré-Bendixson theorem for meromorphic connections on compact Riemann surfaces

ABATE, MARCO;BIANCHI, FABRIZIO
2016-01-01

Abstract

We shall prove a Poincaré–Bendixson theorem describing the asymptotic behavior of geodesics for a meromorphic connection on a compact Riemann surface. We shall also briefly discuss the case of non-compact Riemann surfaces, and study in detail the geodesics for a holomorphic connection on a complex torus.
2016
Abate, Marco; Bianchi, Fabrizio
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/777932
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