Translation Factorable (TF) Surfaces in Three-Dimensional Isotropic Space: Unveiling Future Prospects for Control Systems

Brahim Medjahdi\(^a\), Abdelakder Belhenniche\(^{b,∗}\), Hanifi Zoubir\(^c\)

\(^a\)Ecole Normale Sup´erieure D’Oran, Ahmed Ammour B.P 1063 Saim Mohamed Oran 31003, Algerie.

\(^b\)SYSTEC – Research Center for Systems and Technologies, FEUP – Faculty of Engineering, Porto University, Rua Dr. Roberto Frias sn, 4200-465 Porto, Portugal.

\(^c\)Ecole Nationale Polytechnique d’Oran Maurice Audin, B.P 1523 El M’naouer Oran 31000, Algeria.

Correspondence should be addressed to: medjahdib41@gmail.com, belhenniche@fe.up.pt, zoubirhanifi@yahoo.fr

Copyright © 2023 Brahim Medjahdi, Abdelakder Belhenniche, Hanifi Zoubir. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: Received: 23 July 2023 Accepted: 28 November 2023; Published Online: 07 December 2023.

Abstract

This article introduces the concept of translation-factorable surfaces in the isotropic space 𝕀³ and presents classification theorems for these surfaces based on their isotropic mean and isotropic Gaussian curvatures, considering both zero and nonzero values. Furthermore, an additional investigation is conducted to classify translation-factorable (TF) surfaces in 𝕀³ under the condition H²=K

Keywords:

Isotropic space, translation-factorable surface, mean curvatures, Gaussian curvatures