“Riemannian manifold”的概念、定义、习题解题方法及翻译-数学辞典

单词

Riemannian manifold

释义

Riemannian manifold

A manifold with a metric structure, that is, a first fundamental form, is associated with each set of local coordinates. This means intrinsic properties such as length, angle, area, and Gaussian curvature may be defined. In two dimensions, the first fundamental form is commonly written as

in terms of local coordinates u and v. The length L of a curve (u(t),v(t)) and the area A of a region R are then defined as

If the manifold uses more than one set of coordinates, then transition maps are necessarily isometries so that the metric structure is consistent across the manifold.

随便看

数学辞典收录了4151条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。