S^3中极小曲面和H_1~3中类空极大曲面的局部表示

LOCAL REPRESENTATION OF MINIMAL SURFACES IN S~■ AND SPACELIKE MAXIMAL SURFACES IN H_1~■

利用在适当坐标下S^3中极小曲面的Gauss方程的通解,得到了S^3中极小曲面的局部表示公式,表示量为到S^2的调和映照,通过对S^3中极小曲面Gauss映照的分析,给出了表示量的几何意义.对偶地对H_1~3中的类空极大曲面作了类似的讨论.

This paper represents minimal surfaces in S^3 in terms of harmonic maps to S^3 by using the general solutions of Ganss equation of minimal surfaces in S^(?) under an adapeted tocal coordinates system. Furthermore a geometric explaination to the representative data by analysis the Gauss maps of minimal surfaces in S3 is given. A similar discussion is given on the spacelike maximal surfaces in H_(?)^(?).