Sweeping surface due to rotation minimizing Darboux frame in Euclidean 3-space E 3 " role="presentation"> E 3 E 3 \mathbb{E}^{3}

AIMS Mathematics

article

Maryam T. Aldossary¹  Rashad A. Abdel-Baky² 

[1] Department of Mathematics, College of Science, Imam Abdulrahman bin Faisal University;Department of Mathematics, Faculty of Science, University of Assiut

关键词: Darboux frame;    singularity and convexity;    developable surface;   

DOI  :  10.3934/math.2023021

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

In this paper, we address a new version of Darboux frame using a common tangent vector field to a surface along a curve and call this frame the rotation minimizing Darboux frame (RMDF). Then, we give the parametric equation due to the RMDF frame for a sweeping surface and show that the parametric curves on this surface are curvature lines. Consequently, necessary and sufficient conditions for sweeping surfaces to be developable ruled surfaces are derived. Also, we analyze the conditions when the resulting developable surface is a cylinder, cone or tangential surface. We also provide some examples to illustrate the main results.

【 授权许可】

CC BY