出典:Wiktionary
出典:Wikipedia
出典:『Wikipedia』 (2010/12/18 16:55 UTC 版)
A line element ds (alternatively, infinitesimal element of length) in mathematics can most generally be thought of as the change in a position vector in an affine space expressing the change of the arc length. An easy way of visualizing this relationship is by parametrizing the given curve by Frenet's formulas. As such, a line element is then naturally a function of the metric, and can be related to the curvature tensor.