New models of normal motions of the inextensible curves according to type-1 Bishop frame in ℝ3-Reference-Cited by-同舟云学术

New models of normal motions of the inextensible curves according to type-1 Bishop frame in ℝ3

Published:2020-11-16 Issue:01 Volume:18 Page:2150009
ISSN:0219-8878
Container-title:International Journal of Geometric Methods in Modern Physics
language:en
Short-container-title:Int. J. Geom. Methods Mod. Phys.

Author:

Mohamed Samah Gaber¹²^ORCID

Affiliation:

1. Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box: 400 Al-Ahsa, 31982, Saudi Arabia

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

Abstract

In this work, we compute the time evolution equations (TEEs) of the type-1 Bishop frame of the curve. Also, we study the time evolution equations for type-1 Bishop curvatures (TEEBCs) as a system of partial differential equations (PDEs). Through this study, we give a necessary and sufficient condition for the normal and binormal Bishop velocities. Also, we construct new models of normal motions of inextensible curves in [Formula: see text]. These models are constructed for curves that move according to the type-1 Bishop frame. Also, we make a comparison study between surfaces obtained by the motions of inextensible curves according to the two frames, the type-1 Bishop frame and the Frenet frame.

Publisher

World Scientific Pub Co Pte Lt

Subject

Physics and Astronomy (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219887821500092

Reference14 articles.

1. Congruence Conditions for Nonplanar Developable Surfaces and Their Application to Surface Recognition

2. Developable surfaces in elastoplastic fracture mechanics

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