The developable surfaces with pointwise 1-type Gauss map of Frenet type framed base curves in Euclidean 3-space

AIMS Mathematics

article

Yanlin Li¹  Kemal Eren²  Kebire Hilal Ayvacı³  Soley Ersoy² 

[1] School of Mathematics, Hangzhou Normal University;Department of Mathematics, Faculty of Arts and Sciences, Sakarya University;Department of Mathematics, Faculty of Arts and Sciences, Ordu University

关键词: Gauss maps;    tangent developable surfaces;    focal developable surfaces;    rectifying developable surfaces;    Frenet type frame base curves;    singular points;   

DOI  :  10.3934/math.2023115

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

In this study, the ruled developable surfaces with pointwise 1-type Gauss map of Frenet-type framed base (Ftfb) curve are introduced in Euclidean 3-space. The tangent developable surfaces, focal developable surfaces, and rectifying developable surfaces with singular points are considered. Then the conditions for the Gauss map of these surfaces to be pointwise 1-type are obtained separately. In order to form a basis for the study, first, the basic concepts related to the Ftfb curve and the Gauss map of a surface are recalled. Later, the necessary and sufficient conditions are found for these surfaces to be of the pointwise 1-type of the Gauss map. Finally, examples for each type of these surfaces are given, and their graphics are illustrated.

【 授权许可】

CC BY