Weingarten Rotation Surfaces in 3-dimensional de Sitter Space

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Author(s) : Liu Huili

Preprint series : J. Of Geometry

MSC 2000

53C50 Lorentz manifolds, manifolds with indefinite metrics
52C20 Tilings in $2$ dimensions
53C40 Global submanifolds

Abstract :
In the 3-dimensional de Sitter Space $\sh^3_1$, a surface is said to be a spherical (resp. hyperbolic or parabolic) rotation surface, if it is a orbit of a regular curve under the action of the orthogonal transformations of the 4-dimensional Minkowski space $\E_1^4$ which leave a timelike (resp. spacelike or degenerate) plane pointwise fixed. In this paper, we give all spacelike and timelike Weingarten rotation surfaces in $\sh^3_1$.

Keywords : Weingarten surface, de Sitter space, rotation surface,principal curvature