The generalized gauss map of minimal surfaces in H3 and H4
The generalized gauss map of minimal surfaces in H3 and H4
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H3 和 H4 中最小曲面的广义高斯图
DOI：
10.1007/bf02590022
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发表时间：
1987
期刊：
影响因子：
--
通讯作者：
P. Simões
中科院分区：
文献类型：
--
作者：
C. C. Góes;P. Simões
本文的目的是建立Riemann曲面M到Qn-2 '的超二次曲面i ~ pn-Iz+，，，+znzn = 0的C映射是M到H和H（分别为3维和4维双曲空间）的极小共形浸入的广义Gauss映射3的条件，以双曲空间的上半超平面为模型，利用欧氏度量和双曲度量在M上通过浸入导出的度量之间的共形性，我们可以采用霍夫曼和奥瑟曼[HO，2]发展的理论来获得条件，
The object of this paper is to establish conditions for a C map of a Riemann surface M into Qn-2'the hyperquadric ii~ pn-I z+,,,+ znz n= 0 of, to be the generalized Gauss map 3 of a minimal conformal immersion of M into H and H, the hyperbolic space of dimensions three and four respectively, Using the upper half-hyperplane as model for the hyperbolic space and exploiting the conformality between the metrics induced on M, by'the euclidean metric and the hyperbolic metric through the immersion, we can adapt the theory developed by Hoffman and Osserman [HO, 2] to obtain the conditions,