刘会立
主要研究领域为黎曼与伪黎曼几何,仿射与共形微分几何,信息与计算几何等
个性化签名
- 姓名:刘会立
- 目前身份:
- 担任导师情况:
- 学位:
-
学术头衔:
博士生导师, 优秀教师/优秀教育工作者
- 职称:-
-
学科领域:
计算机软件
- 研究兴趣:主要研究领域为黎曼与伪黎曼几何,仿射与共形微分几何,信息与计算几何等
刘会立,男,一九五九年出生于辽宁省辽阳市。一九七八年三月入沈阳师范学院(现沈阳师范大学)数学系学习;一九八一年十二月沈阳师范学院本科毕业后留校任教。一九八六年九月入东北工学院(现东北大学)数学系攻读硕士学位,研究方向:微分几何;一九八八年十二月东北工学院硕士毕业后留校任讲师,从事数学教学和现代微分几何与应用的研究工作。一九九三年接受德国柏林工业大学数学系的伍德. 西蒙 (Udo Simon) 教授的邀请,到柏林工业大学 (Technische Universitaet Berlin) 数学系,承担由德意志研究联合会 (Deutsche Forschungsgemeinschaft) 资助的科研项目的研究工作。一九九六年在柏林工业大学获得博士学位,然后从事科研与教学工作。一九九七年六月末回到东北大学数学系,同年六月破格直接晋升为正教授。发表论文50余篇,获省部级一等奖、三等奖各一项,同德国、日本、韩国等国的几何学家有合作关系。主要研究领域为黎曼与伪黎曼几何,仿射与共形微分几何,信息与计算几何等。获教育部“资助优秀年轻教师基金”、国家自然科学基金、辽宁省自然科学基金等科研基金资助。政府特殊津贴获得者,“计算机软件与理论”博士导师。
-
主页访问
2822
-
关注数
0
-
成果阅读
594
-
成果数
13
【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
-
72浏览
-
0点赞
-
0收藏
-
0分享
-
129下载
-
0评论
-
引用
【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.,
-
51浏览
-
0点赞
-
0收藏
-
0分享
-
161下载
-
0评论
-
引用
【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.,
-
41浏览
-
0点赞
-
0收藏
-
0分享
-
143下载
-
0评论
-
引用
【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.
-
47浏览
-
0点赞
-
0收藏
-
0分享
-
130下载
-
0评论
-
引用
【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
-
91浏览
-
0点赞
-
0收藏
-
0分享
-
109下载
-
0评论
-
引用
【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.,
-
27浏览
-
0点赞
-
0收藏
-
0分享
-
73下载
-
0评论
-
引用
【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.
-
31浏览
-
0点赞
-
0收藏
-
0分享
-
73下载
-
0评论
-
引用
【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.,
-
64浏览
-
0点赞
-
0收藏
-
0分享
-
86下载
-
0评论
-
引用
【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.,
-
33浏览
-
0点赞
-
0收藏
-
0分享
-
128下载
-
0评论
-
引用
【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.
-
35浏览
-
0点赞
-
0收藏
-
0分享
-
81下载
-
0评论
-
引用