流形及其附加结构

Manifolds and Their Additional Structures

从附加结构的角度将流形的多种概念有机地串联起来,并给出了一种直观理解流形、微分流形等抽象概念的新颖方式.同时,本文阐述了微分几何的主要特点、思想,介绍了与附加结构相关的流形分类问题、Poincare猜测等的研究情况.

We organize the concepts of a variety of manifolds from the perspective of additional structures.And we give a new manner to understand the concepts of manifold and differential manifold.Furthermore,we show the characteristic of differential geometry,and present the research of additional structures of manifolds,such as the classification problem of manifolds,Poincare conjecture.