The Principal Curvatures of A Kind of Weingarten Surfaces

摘要

In this paper, we mainly discuss a new kind of Weingarten surfaces. Firstly, we introduce the construction of this kind of surfaces. Then we study the properties of the principal curvatures of them and obtain a differential relationship between them. Thirdly, we investigate the existence of this kind of W-surface of which the principal curvatures satisfy a differential relationship. At last, we present two examples of the kind of W-surface.