拓扑流形

本文讨论了拓扑流形上Fb的整系数同调群和F的拓扑临界点的不变量间的关系。

In this paper we discuss the relation between the integer homology group of F_b on topological manifold and the invariants of topologically critical point of F.

拓扑流形上Fréchet空间的道路连通分支

Pathwise Connected Components of Fr é chet Space on Topological Manifold

反之，对于紧致拓扑流形，能否由基本群决定在它上面是否容许有非正曲率的黎曼度量？

Can the fundamental groups of any compact topological manifold determin that it admits a non-positively curved Riemannian metric ?

开流形的曲率与拓扑及子流形几何

The Curvature and the Topology of Open Manifolds and the Geometry of Submanifolds

若宇宙空间是拓扑紧化流形，例如三维环面，则类星体红移分布中的周期性即可加以解释。

The periodicity in the distribution of quasar redshifts is interpreted assuming that the cosmological space is a topologically compactified manifold like three dimensional torus .

称一个抽象拓扑空间为流形，若该空间中每一点都在局部上与欧氏空间中的开集同胚。

We say that an abstract topological space is a manifold if each point in the space has a neighbourhood which is homeomorphic to an open subset of Euclid space .

提出一种基于拓扑信息衡量模型流形整体性质的方法EPTIC（Euler-PoincareTopologyInformationCriterion）。

A method EPTIC ( Euler-Poincare Topology Information Criterion ) using topology information to measure the global property of the model manifold is proposed .

在圆柱和上半平面域拓扑积的特征流形上引入一组奇性积分算子M~2，由此来讨论该区域的Dirichlet问题和Neumann问题的解。

This paper established a group of real singular integral operators on characteristic manifold of topological product of cylindrical and half-plane domains , by which it discussed the solutions of Dirichlet-problem and neumann-problem on this domains .

广义有理参数曲线曲面定义在与控制网格拓扑同胚的微分流形上，以高度一般的势函数为基函数，其控制网格可以是任意的一维拓扑流形和二维可定向拓扑流形。

In the framework , a control mesh may be arbitrary one-dimensional or two-dimensional orientated topological manifold , and the curve or surface is defined on differential manifold homeomorphic to the control mesh with a potential function as its basis functions .