Riemann surface with almost positive definite metric  

作　　者：陈志国 

机构地区：[1]Department of Mathematics Zhejiang University

出　　处：《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》2005年第7期747-749,共3页浙江大学学报（英文版）A辑（应用物理与工程）

基　　金：Project (No. 10101023) supported by the National Natural Science Foundation of China

摘　　要：In this paper, we consider and resolve a geometric problem by using μ（z）-homeomorphic theory, which is the generalization of quasiconformal mappings. A sufficient condition is given such that a Ct-two-real-dimensional connected orientable manifold with almost positive definite metric can be made into a Riemann surface by the method of isothermal coordinates. The result obtained here is actually a generalization of Chern＇s work in 1955.In this paper, we consider and resolve a geometric problem by using μ(z)-homeomorphic theory, which is the generalization of quasiconforrnal mappings. A sufficient condition is given such that a C1-two-real-dimensional connected orientable manifold with almost positive definite metric can be made into a Riemann surface by the method of isothermal coordinates. The result obtained here is actually a generalization of Chern's work in 1955.

关 键 词：Quasiconformal mapping.μ（z）-homeomorphisms Beltrami equation Isothermal coordinates 

分 类 号：O186.12[理学—数学]