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.File in questo prodotto:
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