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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】Conformal Structure in Affne Geometry: Complete Tchebychev Hypersurfaces
刘会立, Huili Liu, Udo Simon, Changping Wang**
Abh. Math. Sem. Univ. Hamburg 66 (1996), 249-262,-0001,():
-1年11月30日
We give a conformal classification of affine-complete centroaffne Tchebychev hypersurfaces recently introduced by Liu and Wang. This classifica-tion is based on partial differential equations known from conformal Riemannian geometry. Moreover we investigate Tchebychev hyperovaloids and generalize the classical theorem of Blaschke and Deicke on a
conformal differential equation,, centroaffine Tchebychev hypersur-face,, affine spheres.,
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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】Centroaffine Surfaces with parallel traceless Cubic Form
刘会立, Huili Liu, Changping Wang†
Bull. Belg. Math. Soc. 4 (1997), 493-499,-0001,():
-1年11月30日
In this paper, we classify the centroa ne surfaces with parallel cubic Simon form and the centroa ne minimal surfaces with complete positive de nite at metric.
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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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