Research ArticleNo Access

Sweeping surfaces according to type-2 Bishop frame in Euclidean 3-space

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

and

Mathematical Science Department, Faculty of Science, Princess Nourah bint Abdulrahman University, Riyadh 11546, Saudi Arabia

E-mail Address: fyalmofarrah@pnu.edu.sa

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https://doi.org/10.1142/S1793557121501849Cited by:2 (Source: Crossref)

Abstract

This work is concerned with the study of the kinematic-geometry of a special kind of tube surfaces, so-called sweeping surface in Euclidean 3-space $𝔼^{3}$ . It is generated by a plane curve moving through space such that the movement of any point on the surface is always orthogonal to the plane. In particular, the type-2 Bishop frame is considered and some important theorems are obtained. Also, the problem of singularity and convexity of such sweeping surface is discussed. Finally, an application is presented and plotted using computer aided geometric design.

Communicated by W. S. Cheung

Keywords:

AMSC: 53A04, 53A05, 53A17

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