On curvatures and points of the translation surfaces in Euclidean 3-space
Ali, A., Abdel Aziz, H., Sorour, A. (2015). On curvatures and points of the translation surfaces in Euclidean 3-space. EKB Journal Management System, 23(1), 167-172. doi: 10.1016/j.joems.2014.02.007
Ahmad T. Ali; H.S. Abdel Aziz; Adel H. Sorour. "On curvatures and points of the translation surfaces in Euclidean 3-space". EKB Journal Management System, 23, 1, 2015, 167-172. doi: 10.1016/j.joems.2014.02.007
Ali, A., Abdel Aziz, H., Sorour, A. (2015). 'On curvatures and points of the translation surfaces in Euclidean 3-space', EKB Journal Management System, 23(1), pp. 167-172. doi: 10.1016/j.joems.2014.02.007
Ali, A., Abdel Aziz, H., Sorour, A. On curvatures and points of the translation surfaces in Euclidean 3-space. EKB Journal Management System, 2015; 23(1): 167-172. doi: 10.1016/j.joems.2014.02.007

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

Journal of the Egyptian Mathematical Society
Volume 23, Issue 1, 2015, Page 167-172  XML PDF (425.96 K)
Document Type: Original Article
DOI: 10.1016/j.joems.2014.02.007
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Authors
Ahmad T. Ali* 1, 2; H.S. Abdel Aziz3; Adel H. Sorour3
1King Abdul Aziz University, Faculty of Science, Department of Mathematics, PO Box 80203, Jeddah 21589, Saudi Arabia
2Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City, 11884 Cairo, Egypt
3Department of Mathematics, Faculty of Science, Sohag University, 82524 Sohag, Egypt
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
Translation surfaces; Gaussian and mean curvatures; Euclidean 3-space
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