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arXiv · 1406.6944

A Poincar\'e-Bendixson theorem for meromorphic connections on Riemann surfaces

Marco Abate·Fabrizio Bianchi
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Abstract

We prove a Poincar\'e-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.

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Marco Abate, Fabrizio Bianchi. 2014-06-26. A Poincar\'e-Bendixson theorem for meromorphic connections on Riemann surfaces. https://arxiv.org/abs/1406.6944

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