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›› 2009, Vol. 26 ›› Issue (2): 185-193.DOI: 10.7523/j.issn.2095-6134.2009.2.006

• Research Articles • Previous Articles     Next Articles

On the character 1-form of an HCMU metric

WU Ying-Yi   

  1. School of Mathematical Sciences, Graduate University of the Chinese Academy of Sciences, Beijing 100049, China
  • Received:2008-07-11 Revised:2008-09-09 Online:2009-03-15
  • Supported by:

    supported in part by the President Fund of GUCAS 

Abstract:

An HCMU metric is a kind of extremal metric with conical singularities on a Riemann surface. It can be characterized by a meromorphic 1-form. In this paper we give some important properties of this meromorphic 1-form. As an application we prove the sufficient and necessary condition of the Gauss curvature of an HCMU metric being smooth.

Key words: extremal metric, HCMU metric, character 1-form

CLC Number: