ON CURVES AND TUBES IN $\mathbb{R}^n$
Differential Geometry
2020-11-23 v1
Abstract
In this paper, we present a new explicit formula for the curvatures of a regular curve with an arbitrary parameter in the Euclidean space , , expressed only in terms of its derivatives. We introduce also the notion of tube with arbitrary cross sections around a curve for which we calculate the volume and give a generalization for the second theorem of Pappus. The first theorem of Pappus is obtained for sphere tubes in arbitrary dimension.
Keywords
Cite
@article{arxiv.2011.10116,
title = {ON CURVES AND TUBES IN $\mathbb{R}^n$},
author = {J. Adonai P. Seixas and Isnaldo Isaac Barbosa},
journal= {arXiv preprint arXiv:2011.10116},
year = {2020}
}