The total absolute curvature of closed curves in Riemannian manifolds
The total absolute curvature of closed curves in Riemannian manifolds
复制标题
黎曼流形中闭合曲线的总绝对曲率
DOI：
10.4310/jdg/1214432100
复制
发表时间：
1974
期刊：
影响因子：
--
通讯作者：
C. Hsiung
中科院分区：
文献类型：
--
作者：
F. Brickell;C. Hsiung
本文讨论了关于欧几里德空间中闭曲线总绝对曲率的Fenchel [3]， Milnor [5]， Fary[2]定理的一些推广。得到了具有非正截面曲率的完全单连通黎曼n流形上闭曲线的一个定理，并在曲率为常数时得到了更为精确的结果。本文采用重复指标求和约定，除另有说明外，所有指标取1，，n。
This paper is concerned with some extensions of the theorems of Fenchel [3], Milnor [5], Fary [2] on the total absolute curvature of closed curves in euclidean space. We obtain a theorem for closed curves in a complete simply connected riemannian n-manifold with nonpositive sectional curvature, and this leads to more precise results when the curvature is constant. Throughout this paper the summation convention for repeated indices is used, and all indices take the values 1, , n unless stated otherwise.
影响因子：
4.9
作者：
MILNOR, JW
通讯作者：
MILNOR, JW