ON CURVES AND TUBES IN $\mathbb{R}^n$

J. Adonai P. Seixas; Isnaldo Isaac Barbosa

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arXiv · 2011.10116

ON CURVES AND TUBES IN $\mathbb{R}^n$

J. Adonai P. Seixas·Isnaldo Isaac Barbosa

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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 $\mathbb{R}^n$, $n\geq 2$, 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.

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BibTeX RIS

J. Adonai P. Seixas, Isnaldo Isaac Barbosa. 2020-11-19. ON CURVES AND TUBES IN $\mathbb{R}^n$. https://arxiv.org/abs/2011.10116

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