Journal of Prime Research in Mathematics

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:,,


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


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