E^3中特殊Weingarten曲面的无穷小等距

On Infinitesimal Isometric Deformations of Special Weingarten surfaces in E￣3

Ａ·［１］用拟解折函数方法研究了Ｅ￣３中凸曲面的无穷小等距变形，得到了一些整体结果。本文用类似的万法讨论了Ｅ￣３中另一类曲面——特殊Ｗｅｉｎｇａｒｔｅｎ曲面的无穷小Ⅰ（Ⅱ，Ⅲ）－等距变形，给出了它们作为无穷小刚体运动的条件。

A. Svec studied infinitesimal isometric deformations of convex surfaces inE￣3 and deduced some global properties of such a deformation by the method of quasi-analytic function. This paper discusses the infinitesimal isometric deformations ofanother class of surfaces,special weingarten surfaces,by a similar approach,and the conditions under which those deformations redude to an infinitesimal rigid body motion are given.