Seminar | Institute of Mathematical Sciences
Time：10:10-11:10, April 26, Friday
Location：Room 302, Library
Speaker: Jijian Song, Tianjin University
Abstract: A cone spherical metric on a compact Riemann surface is a conformal metric of Gaussian curvature one which has only finitely many conical singularities. The singularities of the metric can be described by a real divisor with coefficients greater than 1. An open problem is whether there exists a cone spherical metric for any properly given Riemann surface and real divisor D such that the singularities of the metric are represented by the divisor D. By using projective structures, I will give a correspondence between cone spherical metrics representing divisors of integral coefficients and vector bundles of rank 2 on Riemann surfaces of genera greater than one. In particular, for any given stable vector bundle of rank 2 and a line sub-bundle of it, we could construct an irreducible metric on the underlying surface. This is a joint work with Lingguang Li and Bin Xu.