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2019•Journal of Applied and Computational MathematicsRequires access

Some Characterizations of Involute-Evolute Curve Couple in the Hyperbolic Space

Abdel-Aziz Hs, Saad Mk, Abdel-Salam Aa

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Abstract

This paper aims to show that Frenet apparatus of an evolute curve can be formed according to apparatus of the involute curve in hyperbolic space. We establish relationships among Frenet frame on involute-evolute curve couple in hyperbolic 2-space, hyperbolic 3-space and de Sitter 3-space. Finally, we illustrate some numerical examples in support our main results.

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What this paper is about

This paper aims to show that Frenet apparatus of an evolute curve can be formed according to apparatus of the involute curve in hyperbolic space. We establish relationships among Frenet frame on involute-evolute curve couple in hyperbolic 2-space, hyperbolic 3-space and de Sitter 3-space. Finally, we illustrate some numerical examples in support our main results.

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Available abstract

This paper aims to show that Frenet apparatus of an evolute curve can be formed according to apparatus of the involute curve in hyperbolic space. We establish relationships among Frenet frame on involute-evolute curve couple in hyperbolic 2-space, hyperbolic 3-space and de Sitter 3-space. Finally, we illustrate some numerical examples in support our main results.

Key concepts: Frenet–Serret formulas, Involute, Space (punctuation), Frame (networking), Mathematics, Mathematical analysis, Hyperbolic function, Geometry

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Some Characterizations of Involute-Evolute Curve Couple in the Hyperbolic Space — Research Paper | ScholarLens