On the maximal number of exceptional values of Gauss maps for various classes of surfaces
On the maximal number of exceptional values of Gauss maps for various classes of surfaces
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DOI：
10.1007/s00209-012-1115-8
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发表时间：
2012-05
影响因子：
0.8
通讯作者：
Y. Kawakami
中科院分区：
文献类型：
--
作者：
Y. Kawakami
本文的主要目的是揭示空间形式中几类浸入曲面（如欧氏空间中的完备极小曲面、仿射空间中的弱完备非正常仿射球面和双曲空间中的弱完备平坦曲面）的Gauss映射的极大例外值个数的几何意义.为此，我们给出了开黎曼曲面上给定共形度量的有效曲率界。
The main goal of this paper is to reveal the geometric meaning of the maximal number of exceptional values of Gauss maps for several classes of immersed surfaces in space forms, for example, complete minimal surfaces in the Euclidean three-space, weakly complete improper affine spheres in the affine three-space and weakly complete flat surfaces in the hyperbolic three-space. For this purpose, we give an effective curvature bound for a specified conformal metric on an open Riemann surface.