车比雪夫坐标网的性质与极小曲面

Prof、S、S Chern和Wang Baoqin等利用曲面上渐近曲线网和车比雪夫网的关系,实现了在高斯曲率K=常数的二曲面之间的“Bachlund”变换这是曲面的变换论在偏微分方程论中的重要应用。本文旨在介绍并探索了车比雪夫网的一些性质,可供研究曲面变换论的参考。最后,并探讨了曲面的坐标网为半车比雪夫网与极小曲面的一些关系。

THE PROPERTY OF CHEBYSHEV NET AND MINIMAL SURFACE

The professors S.S. Chern and Wang Baoqin accomplished a Backlund transforms tion between two surfaces of Gaussian curvature k=constant with the relation between the asymptotic net and Chebyshev net of surface. This is the important application of the transformatise theory of surfaces in the theory of partical differential equation. The purpose of this paper is to introduce and explore some pcoperties of Chebyaaev Tshev net whicn are refereaced by inveatigating stransformative theory of surface, Finally, some relations are explored between the half Chebyshev net of sarface and minimal urface