双曲空间

·给出了代数双曲空间的拟Legendre基在反函数逼近和等距曲线逼近上的应用。

· The applications of the quasi-Legendre basis defined in the algebraic hyperbolic space in the inversion approximation and offsetting are given in this dissertation .

给出了双曲空间在上半空间模型下的图状超曲面的概念，提出并研究了双曲空间的图状超曲面的Bernstein问题。

In this paper , with respect to the upper halfspace model , the concept of graph-like hypersurfaces in hyperbolic space is defined , the Bernstein problem of graph-like hypersurfaces in hyperbolic space is formed and investigated .

双曲空间H￣3中广义全拟脐超曲面也是全测地的。

The generalized totally quasi-umbilical submanifold in hyperbolic spaces in also totally geodesic .

本文借助于递推的方法给出了在代数双曲空间Hn上以积分迭代形式定义的HPB-Spline基的矩阵表示。

This paper presents the matrix representation for the HP B-Spline basis in a recursive way , which is generated over the algebraic space H_n .

在第三章中，本文介绍了几类特殊的酉群和双曲空间上酉群U（2n）（R，A）的基本子群的正规性定理。

In Chapter ⅲ, we introduce some special case of Unitary groups , and give out the normality of the elementary group of hyperbolic Unitary group .

3维双曲空间中给定平均曲率曲面的Weierstrass表示

Weierstrass representation for surfaces of prescribed mean curvature in the hyperbolic 3-dimensional space

其次，运用度量几何的经典方法考察了度量空间（包括双曲空间和Banach空间）中有限点集的费马点的唯一性。

Secondly , we discussed the uniqueness of Fermat points of finite point sets in some metric spaces ( including hyperbolic spaces and Banach spaces ) .

在第三章证明了构形空间的Lapace算子在等距映射提升下的不变性，并把二维双曲空间的Heck算子推广到构形空间。

In chapter three , we obtain invariance for Laplace operator on the configuration space over a Riemannian manifold in lifting of isometric mapping , we also generalization Heck operator of hyperbolic plane to the configuration space over a hyperbolic plane .

双曲空间中的紧致超曲面在平均曲率下的形变

Deforming Compact Hypersurfaces in a Hyperbolic Space by Their Mean Curvature

双曲空间中三种模型的测地线研究

The study of geodesic of three patterns in hyperbolic space

双曲空间上超布朗运动的范围

The Range of Super - Brownian Motions on Hyperbolic Space

复双曲空间中的直纹实超曲面

Ruled Real hypersurfaces in complex hyperbolic space CH ~ n

三维双曲空间中平行曲面族的两个定理

Two theorems for the families of parallel surfaces in ih ~ 3

研究复双曲空间中的全纯曲线。

In this article holomorphic curves in the complex hyperbolic space are discussed .

代数双曲空间中两组基的矩阵表示及其转换矩阵

Matrix Representation and Conversion Matrix for Two Bases of the Algebraic Hyperbolic Space

基于双曲空间的层次信息可视化方法研究

Research on Hierarchical Information Visualization Based on Hyperbolic Space

曲面到复双曲空间的调和映射

Harmonic maps of surfaces into complex hyperbolic spaces

伪黎曼球面和伪双曲空间的子流形

Submanifolds of Pseudo-Riemannian Sphere and Pseudo-Hyperbolic Space

复双曲空间中的离散群及复双曲流形的体积的相关问题

Discrete Groups in Complex Hyperbolic Space and the Problems on the Volumes of the Manifold

典型域上的调和函数论（Ⅰ）&矩阵双曲空间的调和函数

Theory of harmonic functions of classical domains (ⅰ) & harmonic functions in the hyperbolic space of matrices

双曲空间上等距子群的离散性与四点对的模空间

The Discreteness of Isometric Subgroups Acting on Hyperbolic Space and the Moduli Space of Quadruples of Points

这双曲空间的发现开创了数学领域，就是所谓的非欧几里德几何；

The discovery of hyperbolic space ushered in the field of mathematics that is called non-Euclidean geometry .

关于双曲空间中的椭圆

On ellipse in Hyperbolic Spaces

在双曲空间中，对椭圆的周长及平均绝对曲率做出细致考察。

Geometric data of ellipse in hyperbolic space are considered , such as perimeter and mean absolute curvature .

定义了双曲空间上的度量平均的概念，得到了关于度量平均的几个不等式。

The definition of metric averaging in hyperbolic space is given a few inequalities of metric averaging are obtained .

双曲空间H~（n+p）（-1）中具有常数量曲率的完备子流形

Complete Submanifolds in Hyperbolic Space H ~ ( n + p )( - 1 ) With Constant Scalar Curvature

实验表明，基于双曲空间的最短路径查询算法的效率和准确性都比较高。

Experiments are done to verify the shortest path query method based on hyperbolic space having a high efficiency and accuracy .

多个复变数函数论&Ⅰ.矩阵的双曲空间中的一完整正交函数系

On the theory of functions of several complex variables ,ⅰ & a complete orthonormal system in the hyperbolic space of matrices

而且球面和双曲空间中的半对称或半平行的理想超曲面均为最多具有两个不同常主曲率的等参子流形。

Moreover , ideal hypersurfaces in a nontrivial real-space-form are proved to be isoparametric submanifolds with at most two distinct principal curvatures .

首先介绍了已有的最短路径查询算法，然后设计了基于双曲空间的最短路径查询算法。

Firstly , the existing shortest path query methods are introduced . Then a shortest path query method based on hyperbolic space is designed .