| A Kind of Weingarten Surfaces in $E^3$ with Prescribed Principal Curvatures |
| Received:April 08, 2008 Revised:July 07, 2008 |
| Key Words:
the principal curvatures the Weingarten surfaces the rotation surfaces.
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| Fund Project:Supported by the SDFDP (Grant No.20050141011) and the MATH X Project Offered by Dalian University of Technology (Grant No.MXDUT073005). |
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| Abstract: |
| In this paper, we construct a kind of Weingarten surfaces in $E^3$ and study its geometric properties. We first derive an explicit differential 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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2010.04.006 |
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