On curvatures and points of the translation surfaces in Euclidean 3-space

Ali, Ahmad T.; Abdel Aziz, H.S.; Sorour, Adel H.

doi:10.1016/j.joems.2014.02.007

On curvatures and points of the translation surfaces in Euclidean 3-space

Document Type : Original Article

Authors

¹ King Abdul Aziz University, Faculty of Science, Department of Mathematics, PO Box 80203, Jeddah 21589, Saudi Arabia

² Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City, 11884 Cairo, Egypt

³ Department of Mathematics, Faculty of Science, Sohag University, 82524 Sohag, Egypt

10.1016/j.joems.2014.02.007

Abstract

In this paper, translation surfaces generated by two arbitrary space curves in 3-dimensional Euclidean space have been investigated. Furthermore, a classification of some special points
on these surfaces have been given. Moreover, we have obtained the associated geometric attributes
for these surfaces, e.g. the Gaussian curvature and the mean curvature. Finally, some important
results and examples that show the idea were presented.

Keywords