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【期刊论文】Classiflcation of flat indeflnite Equi-centroaffnely Homogeneous Surfaces in R4
刘会立, Huili Liu*
Results in Mathematics 29 (1996),-0001,():
-1年11月30日
A nondegenerate equi-centroaffne surface in R4 is called homoge-neous if for any two points p and q on the surface there exists an equi-centroaffne transformation in R4 which takes the surface to itself and takes p to q. In this paper we classify the equi-centroaffnely homogeneous surfaces with flat indefinite metric in R4 up to centroa
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【期刊论文】Cubic Form Methods and Relative Tchebychev Hypersurfaces
刘会立, A.-M. LI, H. L. LIU, A. SCHWENK-SCHELLSCHMIDT, U. SIMON and C. P. WANG*
Geometriae Dedicata 66: 203-221, 1997.,-0001,():
-1年11月30日
We introduce the concept of a relative Tchebychev hypersurface which extends that of affine spheres in equiaffine geometry and also that of centroaffine Tchebychev hypersurfaces and give partial local and global classifications for this new class. Our tools concern a new operator and interesting properties of the traceless part of the cubic form.
Tchebychev hypersurface,, relative geometry,, hyperovaloid,, cubic form.,
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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】Classification of Surfaces in R3 which are centroaffine-minimal and equiaffine-minimal
刘会立, Huili Liu*
Bull. Belg. Math. Soc. 3 (1996), 577-583,-0001,():
-1年11月30日
We classify all surfaces which are both, centroa ne-minimal and equia neminimal in R3.
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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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