@article{Khalifa Saad2024, 
author = {M. Khalifa Saad and Nural Yüksel and Nurdan Oğraş and Fatemah Alghamdi and A. A. Abdel-Salam},
title = {Geometry of tubular surfaces and their focal surfaces in Euclidean 3-space},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {5},
pages = {12479-12493},
keywords = {tubular surfaces, focal surfaces, modified orthogonal frame},
url = {https://www.sciopen.com/article/10.3934/math.2024610},
doi = {10.3934/math.2024610},
abstract = {In this study, we examined the focal surfaces of tubular surfaces in Euclidean 3-space        E          3      . We achieved some significant results for these surfaces in accordance with the modified orthogonal frame. Additionally, we proposed a few geometric invariants that illustrated the geometric characteristics of these surfaces, such as flat, minimal, Weingarten, and linear-Weingarten surfaces, using the traditional methods of differential geometry. Additionally, the asymptotic and geodesic curves of these surfaces have been researched. At last, we presented an example as an instance of use to validate our theoretical findings.}
}