论文标题
Riemann表面上的Meromorthic连接的平坦结构
Flat structure of meromorphic connections on Riemann surfaces
论文作者
论文摘要
Abate，Tovena和Bianchi已经研究了紧凑的Riemann表面上的Meromormormorphic Connections的简单的大地测量学限制集。在本文中，我们研究了无限自我隔离的大地测量问题的同样问题。在本文的第一部分中，我们研究了Meromororphic $ k $ differentials，单数平面度量和Meromorormormormormormormormorthic Connections之间的关系。此外，我们证明了一种庞加莱 - 贝德克森定理，用于无限自我互认为与$ g $ monodromy连接的Meromormorphic连接的大地测量学，其中$ \ arg g^k = \ {0 \ {0 \} $ in \ mathbb {n} $中的某些$ k \。
The possible omega limit sets of simple geodesics for meromorphic connections on compact Riemann surfaces have been studied by Abate, Tovena and Bianchi. In this paper, we study the same problem for infinite self-intersecting geodesics. In the first part of the paper we study relation among meromorphic $k$-differentials, singular flat metrics and meromorphic connections. Moreover, we prove a Poincaré-Bendixson theorem for infinite self-intersecting geodesics of meromorphic connections with monodromy in $G$, where $\arg G^k=\{0\}$ for some $k\in\mathbb{N}$.
