Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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M. Abate - F. Bianchi

A Poincaré-Bendixson theorem for meromorphic connections on Riemann surfaces

created by stoppato on 08 Nov 2016
modified by bianchi on 11 Dec 2020


Published Paper

Inserted: 8 nov 2016
Last Updated: 11 dec 2020

Journal: Math. Z.
Volume: 282
Number: 1-2
Pages: 247-272
Year: 2016
Doi: 10.1007/s00209-015-1540-6

ArXiv: 1406.6944 PDF


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.

Tags: FIRB2012-DGGFT

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