Open Access

ARTICLE

Some Geometric Invariants of Pseudo-Spherical Evolutes in the Hyperbolic 3-Space

H. S. Abdel-Aziz¹, M. Khalifa Saad^1,2,*, A. A. Abdel-Salam¹

1 Mathematics Department, Faculty of Science, Sohag University, 82524, Sohag, Egypt .
2 Mathematics Department, Faculty of Science, Islamic University of Madinah, 170 El-Madinah, KSA.

* Corresponding Author: M. Khalifa Saad. Email: .

Computers, Materials & Continua 2018, 57(3), 389-415. https://doi.org/10.32604/cmc.2018.02149

Abstract

In this paper, we study the pseudo-spherical evolutes of curves in three dimensional hyperbolic space. We use techniques from singularity theory to investigate the singularities of pseudo-spherical evolutes and establish some relationships between singularities of these curves and geometric invariants of curves under the action of the Lorentz group. Besides, we defray with illustration some computational examples in support our main results.

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Citations