Hausdorff向量场  

Hausdorff Vector Fields

作　　者：李洪军[1] 

机构地区：[1]西安交通大学数学系

出　　处：《工程数学学报》1997年第4期85-90,共6页Chinese Journal of Engineering Mathematics

摘　　要：讨论了紧流形上的光滑无奇点向量场。建立了光滑无奇点向量场与流形的Ｓ－结构之间的一一对应。把轨道空间是Ｈａｕｓｄｏｒｆ空间的向量场称为Ｈａｕｓｄｏｒｆ向量场。Ｈａｕｓｄｏｒｆ向量场的轨道空间是一个余一维的光滑流形。本文的主要结果是：ｎ－维流形Ｍ上存在Ｈａｕｓｄｏｒｆ向量场的充要条件是Ｍ是某（ｎ－１）－维流形上的光滑Ｓ１－纤维丛。In this paper, we investagate smooth vector fields without critical point on compact manifold. There is a 1-1 correspondence between smooth vector fields without critical point and the S structures on the manifold. A vector field without critical point is called a Hausdorff vector field when its trajectory space is a Hausdorff space. The main result is the following theoerm: there exists a Hausdorff vector fields on an n dimensional manifold M iff M is a smooth S 1 fibre boundle over an (n-1) dimensional manifold.

关 键 词：无奇点向量场 S-结构 纤维丛 豪斯道夫向量场 

分 类 号：O189.34[理学—数学]