关于曲面的高斯像的一个定理

可展曲面是直纹曲面的一种类型,可展曲面就是沿每一条直母线只有一个切平面.通过几何分析方法,讨论了直纹曲面,给出了直纹曲面是可展曲面的一个充分且必要条件.得到直纹曲面是可展曲面,其充要条件是：曲面S的Gauss映射像是一条曲线.并给出这个定理应用的例子.

A Theorem About Curved Surface Gauss Mapping

The developable surface, along every straight line, each with only one tangent plane, is a type of ruled surface. Our purpose is to give a sufficient and necessary condition of the developable surface. We use the methods of geometry analysis to study the ruled surface, and get a sufficient and necessary condition of the developable surface, that is, Gauss Mapping of the Curved Surface is a curve and finally gives an example of this new application of the theorem.