曲线与其曲率圆的位置关系

本文指出文［１］中的不妥之处，给出了曲线与其上任一点处的曲率圆相切的三种不同情形，以及判别不同情形的充分条件．     

常曲率空间中的正曲率子流形

本文研究了常曲率空间子流表余维数减少的问题,说明了在一定条件下,余维数可以减少到１。     

中曲率大于零的非凸曲面

本文研究了曲面的曲率问题.利用积分几何方法和旋转曲面性质,构造出一个欧氏空间R3中紧致光滑的中曲率H大于零的非凸曲面,并得到了关于紧致光滑曲面曲率的几个不等式.     

子流形的测地曲率

该文研究了黎曼齐次空间G/H中子流形M~p和子流形N~q的交M~p∩gN~q的测地曲率,其中g∈G为等距群,并把M~p∩gN~q的第二基本形式表示成M~p和N~q的测地曲率以及它们之间的夹角的组合.     

欧氏空间中子流形的曲率与几何性质

研究了欧氏空间En p中具常数量曲率n(n-1)r的n(n>2)维完备连通子流形,得到了En p截面曲率非负且法联络平坦的完备连通子流形的一个分类定理.     

拟常曲率流形中有平行平均曲率向量的子流形

研究了拟常曲率流形中具有平行平均曲率向量的子流形,给出了两个积分不等式.     

曲面上的曲率新讲

阐述一种讲解曲面上的各种曲率形式的新教学模式.我们利用平面向量分析,矩阵,求导运算等工具推导出所有的结论和公式.这种新观点和方法避免了微分几何传统讲法中使用Weingarten映射及其特征值的思路,而较之更加直观明了.     

de sitter空间中具平行中曲率的完备类空子流形

本文推广了文[1]的结论，证明了de sitter空间Sp^n＋p（c）中具有平行中曲率的n维完备类空子流形的一个刚性定理．     

常曲率空间中具平行平均曲率向量的子流形

本文利用第二基本形式的长度平方和平均曲率的关系研究常曲率空间中具平行平均曲率向量的子流形为全脐的ｐｉｎｃｈｉｎｇ问题，获得了一定条件下的最佳ｐｉｎｃｈｉｎｇ区间，并确定了ｐｈｉｎｃｎｉｎｇ区间端点处对应非全脐子流形的分类．     

Submanifolds with Flat Normal Bundle

Let M be a compact orientable submanifold immersed in a Riemannian manifold of constant curvature with flat normal bundle. This paper gives intrinsic conditions for M to be totally umbilical or a local product of several totally umbilical submanifolds. It is proved especially that a compact hypersurface in the Euclidean space with constant scalar curvature and nonnegative Ricci curvature is a sphere.     

Complete Hypersurfaces with Constant Mean Curvature and Finite Total Curvature

The main result of this paper states that the traceless second fundamental tensor A⁰ of an n-dimensional complete hypersurface M, with constant mean curvature H and finite total curvature, _M |A⁰|ⁿ dv_M < , in a simply-connected space form (c), with non-positive curvature c, goes to zero uniformly at infinity. Several corollaries of this result are considered: any such hypersurface has finite index and, in dimension 2, if H ² + c > 0, any such surface must be compact.     

The Total Mean Curvature of a Complete Noncompact Surface of Nonnegative Curvature in R3

We give a complete classification of complete noncompact oriented surfaces with nonnegative Gaussian curvature and finite total mean curvature in R³.     

双三次Bezier曲面片的光滑拼接

本文根据曲面的总曲率和平均曲率推导出双三次Bezier曲面片拼接的C^2连续条件。     

Indefinite Affine Umbilical Surfaces in R^4

We study surfaces M ² in the four-dimensional affine space equipped with its usual torsion-free connection D and parallel volume form given by the determinant.     

The Reed-Muller Code R(1,7) Is Normal

We prove that the Reed-Muller code R(1,7) is normal. The normality of R(1,7) was a long-standing open question, and has an important consequence in a conjecture about the function t[n,k], the smallest covering radius of any [n,k] binary linear code.     

An optimal rigidity theorem for complete submanifolds in a sphere

It is proved that if M^n is an n-dimensional complete submanifold with parallel mean curvature vector and flat normal bundle in S^n＋p（1）, and if supM S 〈 α（n, H）, where α（n,H）=n＋n^3/2（n-1）H^2-n（n-2）/n（n-1）√n^2H^4＋4（n-1）H^2,then M^n must be the totally urnbilical sphere S^n（1/√1＋H^2）.An example to show that the pinching constant α（n, H） appears optimal is given.     

Spectral Properties of Constant Mean Curvature Submanifolds in Hyperbolic Space

In this work we determine the essential spectrum of the stability operator of a submanifold of the hyperbolic space with constant mean curvature h < 1 and finite total curvature. In some particular cases, we also give a bound on the number of eigenvalues which are below the essential spectrum.     

多复变中正规权Zygmund空间上的几个性质

本文讨论了多复变中单位球上正规权Zygmund空间Z_μ(B)的一些性质.首先给出了Z_μ(B)函数的一种积分表示,接着证明了Z_μ(B)是正规权Bergman空间A_v~1(B)的对偶空间,其对偶对按如下形式给出:■,其中v(p)=(1-ρ~2)~(β+1)μ~(-1)(ρ)(0≤ρ<1)并且β>max{0,b-1}.最后作为积分表示和对偶的一个应用,作者给出了Z_μ(B)中每个函数的一个原子分解.