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【期刊论文】Weingarten rotation surfaces in 3-dimensional de Sitter space
刘会立, Huili Liu* and Guili Liu
J. Geom. 79(2004)156-168,-0001,():
-1年11月30日
In the 3-dimensional de Sitter Space S31, 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 E4 1 which leave a timelike (resp. spacelike or degenerate) plane pointwise fixed. In this paper, we give all spacelike and timelike Weingarten rotation surfaces in S31.
Weingarten surface,, de Sitter space,, rotation surface,, principal curvature.,
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【期刊论文】Translation Surfaces with constant Mean Curvature in 3-dimensional Spaces
刘会立, Huili Liu*
J. Geom. 64 (1999), 141-149,-0001,():
-1年11月30日
We give the classiffcation of the translation surfaces with constant mean curvature or constant Gauss curvature in 3-dimensional Euclidean space E3 and 3-dimensional Minkowski space E31.
Keywords and phrases., Mean curvature,, translation surface,, spacelike surface,, timelike sur-face.,
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33浏览
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【期刊论文】RELATIVE TCHEBYCHEV SURFACES IN R3
刘会立, Huili Liu and Changping Wang
Kyushu J. Math. 50 (1996), 533-540,-0001,():
-1年11月30日
In this paper some interesting global properties of relative Tchebychev sur-faces in R3 are given. Blaschke's characterization of the ovaloid is generalized to relative differential geometry.
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【期刊论文】Mobius Isoparametric Hypersurfaces in Sn+1 with Two Distinct Principal Curvatures
刘会立, Hai Zhong LI), Hui Li LIU), Chang Ping WANG), Guo Song ZHAO)
Acta Mathematica Sinica, English Series July, 2002, Vol. 18, No.3, pp. 437-446,-0001,():
-1年11月30日
A hypersurface x: M → Sn+1 without umbilic point is called a Mobius isoparametric hypersurface if its Mobius form Φ=−ρ−2 Σi(ei(H) + Σj (hij−Hδij)ej(log ρ))θi vanishes and its Mobius shape operator S=ρ−1(S−Hid) has constant eigenvalues. Here {ei} is a local orthonormal basis for I=dx·dx with dual basis {θi}, II =Σ ij hijθi ⊗ θj is the second fundamental form, H=1 n Σi hii, ρ2=n n−1 (||II||2−nH2) and S is the shape operator of x. It is clear that any conformal image of a (Euclidean) isoparametric hypersurface in Sn+1 is a Mobius isoparametric hypersurface, but the converse is not true. In this paper we classify all Mobius isoparametric hypersurfaces in Sn+1 with two distinct principal curvatures up to Mobius transformations. By using a theorem of Thorbergsson [1] we also show that the number of distinct principal curvatures of a compact Mobius isoparametric hypersurface embedded in Sn+1 can take only the values 2, 3, 4, 6.
Mobius geometry,, Isoparametric hypersurface,, Principal curvature
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【期刊论文】Hyperbolic Rotation Surfaces of Constant Mean Curvature in 3-de Sitter Space
刘会立, Huili Liu, Guili Liu
Bull. Belg. Math. Soc. 7 (2000), 455-466,-0001,():
-1年11月30日
In the 4-dimensional Minkowski space R41, a surface is said to be a hyperbolic rotation surface, if it is a orbit of a regular curve under the action of the orthogonal transformations of R41 which leave a spacelike plane pointwise xed. In this paper, we give the totally classi cation of the timelike and spacelike hyperbolic rotation surfaces in 3-dimensional de Sitter space S31.
de Sitter space,, timelike surface,, spacelike surface,, hyperbolic rotation surface,, constant mean curvature surface.,
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