$E^3$中的一类Weingarten曲面

In this paper, we construct a kind of Weingarten surfaces in E3 and study its geometric properties. We first derive an explicit diffierential relationship between the principal curvatures of them. Then we prove an existence theorem of this kind of surfaces with prescribed principal curvatures. At last, we present two examples involving the rotation surfaces as the special case, and present several figures to the second example.