2022 # Family of Surfaces with a Common Special Involute and Evolute Curves

**Abstract:** In this paper, we define the necessary and sufficient conditions for a parametric surface on which both the involute and evolute of any given curve lie to be geodesic, asymptotic and curvature line. Then, the first and second fundamental forms of these surfaces are calculated. By using the Gaussian and mean curvatures, the developability and minimality assumptions are drawn, as well.
Moreover we extended the idea to the ruled surfaces. Finally, we provide a set of examples to illustrate the corresponding surfa…

Help me understand this report

Search citation statements

Paper Sections

Select...

1

1

Citation Types

0

2

0

Year Published

2023

2023

Publication Types

Select...

2

Relationship

0

2

Authors

Journals

(2 citation statements)

0

2

0

“…D and 1 D be tangent, principal normal-like and binormal-like vectors at point () s of a polynomial space curve , respectively, then the Frenet like curve frame is given by matrix form 12 , dd and 3 d are the curvatures of the polynomial curve with the arc-length s (see for more details [7][8][9]), respectively. Let s X and u X be tangent vectors of a surface , X s u , then the normal vector field of the surface , X s u can be defined by…”

confidence: 99%

“…D and 1 D be tangent, principal normal-like and binormal-like vectors at point () s of a polynomial space curve , respectively, then the Frenet like curve frame is given by matrix form 12 , dd and 3 d are the curvatures of the polynomial curve with the arc-length s (see for more details [7][8][9]), respectively. Let s X and u X be tangent vectors of a surface , X s u , then the normal vector field of the surface , X s u can be defined by…”

confidence: 99%

“…To solve this problem, Dede defined the Flc frame for moving polynomial curves [7,8]. The Flc frame [9][10][11][12][13] and ruled surfaces on different frames [14][15][16][17][18][19][20][21][22][23] have been investigated by many researchers. Inspired by these studies, we conducted this research to create a new resource on the subject of surfaces and to form a basis for future studies.…”

confidence: 99%