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

H. S. Abdel-Aziz1, M. Khalifa Saad1,2,*, A. A. Abdel-Salam1

Mathematics Department, Faculty of Science, Sohag University, 82524, Sohag, Egypt .
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.


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.


Cite This Article

H. S. Abdel-Aziz, M. Khalifa Saad and A. A. Abdel-Salam, "Some geometric invariants of pseudo-spherical evolutes in the hyperbolic 3-space," Computers, Materials & Continua, vol. 57, no.3, pp. 389–415, 2018.


This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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