2020/04/06 by Yu Feng, Yiqian Shi, Feng, Yu +5
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2004.02513
openalex publication_date 2020/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a conjecture that the monodromy group of a singular hyperbolic metric on a non-hyperbolic Riemann surface is \it Zariski dense in \rm PSL(2, \Bbb R). By using meromorphic differentials and affine connections, we obtain an evidence of the conjecture that the monodromy group of the singular hyperbolic metric can not be contained in four classes of one-dimensional Lie subgroups of \rm PSL(2, \Bbb R). Moreover, we confirm the conjecture if the Riemann surface is either one of the once punctured Riemann sphere, the twice punctured Riemann sphere, a once punctured torus and a compact Riemann surface.