定向在流形路径上连续延拓的存在唯一性

Existence and uniqueness of continuous continuation of orientation on the manifold path

流形是微分几何中的主要研究对象,流形可根据是否可定向分为可定向流形与不可定向流形,可定向流形与不可定向流形有着诸多不同的性质.定向在流形路径上连续延拓的存在唯一性为可定向这一性质定义的理论基础,利用实变函数、拓扑学相关知识,给出了定向在流形路径上连续延拓存在唯一性的一个证明方法.

The manifold is an important research object in differential geometry,manifolds can be divided into orientable manifolds and non-orientable manifolds according to whether they are orientable or not,orientable manifolds and non-orientable manifolds have many different properties.Existence and uniqueness of continuous continuation of orientation on the manifold path are the theoretical basis of the definition of orientable manifold.A method to prove the existence and uniqueness of continuous continuation of orientation on the manifold path is given by using the knowledge of real variable function and topology.