2019•Journal of the Egyptian Mathematical SocietyOpen access

On involute-evolute curve couple in the hyperbolic and de Sitter spaces

H. S. Abdel-Aziz, M. Khalifa Saad, A. A. Abdel-Salam

Abstract

This paper aims at showing that Frenet apparatus of an evolute curve can be formed in terms of Frenet apparatus of its involute curve in the hyperbolic ( de Sitter ) space. Also, we establish relationships among Frenet frame of the considered curve couple. Finally, we defray some examples to confirm our main results.

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