关于可展曲面的一点注记

A NOTE ON DEVELOPABLE SURFACE

对于R3中任意给定的光滑曲线l ,必存在R3中的可展曲面Σ ,使得l为Σ的曲率线或是测地线 ,也存在R3中的直纹曲面Σ1,使得l为Σ1上的渐近线 .

In this note we prove the fellowing theorems: \ \ Theorem 1\ Given any C 4 space curve l. Then there exists a developable surface Σ, such that curve l be geodesic or curvature line of Σ. \ \ Theorem 2\ Given any C 4 space curve l. Then there exists a ruled surface Σ, such that curve l be asymptotic line of Σ.