On geometry of focal surfaces due to B-Darboux and type-2 Bishop frames in Euclidean 3-space

AIMS Mathematics

Emad Solouma¹  Ibrahim AL-Dayel²  Meraj Khan³ 

[1] 1. Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University, Saudi Arabia 2. Department of Mathematics and Information Science, Faculty of Science, Beni-Suef University, Egypt;1. Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University, Saudi Arabia;3. Department of Mathematics, University of Tabuk, Saudi Arabia;

关键词: euclidean geometry;    focal surface;    type-2 bishop frame;    tubular surface;    b-darboux frame;   

DOI  :  10.3934/math.2022744

来源: DOAJ

【 摘 要 】

In Euclidean 3-space $ {\mathrm{E}}^3 $, a canonical subject is the focal surface of such a cliched space curve, which would be a two-dimensional corrosive with Lagrangian discontinuities. The tubular surfaces with respect to the B-Darboux frame and type-2 Bishop frame in $ {\mathrm{E}}^3 $ are given. These tubular surfaces' focal surfaces are then defined. For such types of surfaces, we acquire some results becoming Weingarten, flat, linear Weingarten conditions and we demonstrate that in $ {\mathrm{E}}^3 $, a tubular surface has no minimal focal surface. We also provide some examples of these types of surfaces.

【 授权许可】

Unknown