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 exi...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.展开更多
基金Supported by the SDFDP (Grant No.20050141011)the MATH+X Project Offiered by Dalian University of Technology (Grant No.MXDUT073005)
文摘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.
