完备连通黎曼流形的等距浸入
Isometric immersions of a complete and connected Riemannian manifold
本文先黎曼流形的一些基本的概念和定理做了一个简要的介绍,然后对子流形的基本情况介绍引出等距浸入的概念。引入了Hideki Omori在黎曼流形上的极大值原理后,然后用这个定理用现代化的数学语言证明了黎曼流形等距浸入的一个基本的定理。对定理中的$R^n$替换成更具一般性的空间加上额外的条件后,就得到了推广后的定理,并用类似的方法给出了证明。
In this paper, some basic concepts and theorems of Riemannian manifolds are introduced briefly, and then the concept of isometric immersion is introduced in oeder to introduce the basic cconcept of submanifolds. After introducing Hideki Omori's maximum principle on Riemannian manifolds, a basic theorem of isometric immersion of Riemannian manifolds is proved by using this theorem with modern mathematical language. By replacing $R^n$in the theorem with a more general space and adding additional conditions, the generalized theorem is obtained, and the proof is given in a similar way.
段久顺、周恒宇
数学
基础数学等距浸入极大值原理第二基本形式截面曲率
Basic mathematicsIsometric immersionMaximun principleSecond fundamental formSectional curvature
段久顺,周恒宇.完备连通黎曼流形的等距浸入[EB/OL].(2023-02-02)[2025-08-18].http://www.paper.edu.cn/releasepaper/content/202302-11.点此复制
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