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.
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Both authors were partially supported by the FIRB 2012 project Differential geometry and geometric function theory. The first author has also been partially supported by GNSAGA (INdAM).
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Abate, M., Bianchi, F. A Poincaré–Bendixson theorem for meromorphic connections on Riemann surfaces. Math. Z. 282, 247–272 (2016). https://doi.org/10.1007/s00209-015-1540-6
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DOI: https://doi.org/10.1007/s00209-015-1540-6