Surface family pair with Bertrand pair as mutual geodesic curves in Euclidean 3-space $ \mathbb{E}^{3} $-Reference-Cited by-同舟云学术

Surface family pair with Bertrand pair as mutual geodesic curves in Euclidean 3-space $ \mathbb{E}^{3} $

Published:2023 Issue:9 Volume:8 Page:20546-20560
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Almoneef Areej A.¹,Abdel-Baky Rashad A.²

Affiliation:

1. Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia

2. Department of Mathematics, Faculty of Science, University of Assiut 71516, Egypt

Abstract

<abstract><p>The main interest of this work is to construct surface family pair with the symmetry of Bertrand pair in Euclidean 3-space $ \mathbb{E}^{3} $. Then, by employing the Serret-Frenet frame, we conclude the sufficient and necessary conditions of surface family pair interpolating Bertrand pair as mutual geodesic curves. Moreover, the conclusion to ruled surface family pair is also obtained. Meanwhile, this work is demonstrated through several examples.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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