scholarly journals Computation of Smarandache curves according to Darboux frame in Minkowski 3-space

2017 ◽  
Vol 25 (4) ◽  
pp. 382-390
Author(s):  
H.S. Abdel-Aziz ◽  
M. Khalifa Saad
Keyword(s):  
Darboux Frame

Minimal surfaces with elastic and partially elastic boundary

2020 ◽  
pp. 1-22
Author(s):  
Bennett Palmer ◽  
Álvaro Pámpano
Keyword(s):  
Linear Combination ◽  
Minimal Surfaces ◽  
Elastic Boundary ◽  
Darboux Frame ◽  
Special Case

We study equilibrium surfaces for an energy which is a linear combination of the area and a second term which measures the bending and twisting of the boundary. Specifically, the twisting energy is given by the twisting of the Darboux frame. This energy is a modification of the Euler–Plateau functional considered by Giomi and Mahadevan (2012, Proc. R. Soc. A 468, 1851–1864), and a natural special case of the Kirchhoff–Plateau energy considered by Biria and Fried (2014, Proc. R. Soc. A 470, 20140368; 2015, Int. J. Eng. Sci. 94, 86–102).

Involute-evolute d-curves in Minkowski 3-space E 3 1

2021 ◽  
Vol 39 (1) ◽  
pp. 147-156
Author(s):  
Fatma Almaz ◽  
Mihriban Alyamaç Kulahci
Keyword(s):  
Darboux Frame

In this paper, we examine the notion of the involute-evolute curves for the curves lying the surfaces in Minkowski 3-space E3 1 . We call these new associated curves as involute-evolute and by using the Darboux frame of the curves. We give the representation formulae for spacelike curves in Minkowski 3-space E3 1 and using this formulae we give some characterizations of these curves. Besides, we find the relations between the normal curvatures, the geodesic curvatures and the geodesic torsions of these curves.

scholarly journals An approach to energy and elastic for curves with extended Darboux frame in Minkowski space

2020 ◽  
Vol 5 (2) ◽  
pp. 1025-1034
Author(s):  
Talat Körpinar ◽  
◽  
Yasin Ünlütürk ◽  
Keyword(s):  
Minkowski Space ◽  
Darboux Frame

scholarly journals N-BISHOP DARBOUX VECTOR OF A TIMELIKE CURVE IN MINKOWSKI 3-SPACE

2020 ◽  
Vol 20 (3) ◽  
pp. 519-528
Author(s):  
HATICE KUSAK SAMANCI
Keyword(s):  
Differential Geometry ◽  
Minkowski Space ◽  
Timelike Curve ◽  
Rotation Vector ◽  
Effective Alternative ◽  
Darboux Vector ◽  
Bishop Frame ◽  
Alternative Approach ◽  
Darboux Frame ◽  
First Time

It is known that a Bishop frame of a curve is one of the effective alternative approach in the differential geometry. Recently, several important works have been done about the Bishop frames. The aim of our paper is to investigate the N-Bishop frame for timelike curves in Minkowski space. We define the N-Bishop frame for the timelike curve in Minkowski space. Then, we consider some properties of the frame. Moreover, we describe the N-Bishop Darboux frame for the first time. Additionally, we compute some geometrical characterizations for the N-Bishop Darboux axis and momentum rotation vector.

scholarly journals Harmonic Evolute Surface of Tubular Surfaces via B -Darboux Frame in Euclidean 3-Space

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
E. M. Solouma ◽  
Ibrahim AL-Dayel
Keyword(s):  
Mean Curvature ◽  
Normal Vector ◽  
Unit Normal Vector ◽  
Geometric Characteristics ◽  
Darboux Frame ◽  
Tubular Surfaces ◽  
Unit Normal

In this article, we look at a surface associated with real-valued functions. The surface is known as a harmonic surface, and its unit normal vector and mean curvature have been used to characterize it. We use the Bishop-Darboux frame ( B -Darboux frame) in Euclidean 3-space E 3 to study and explain the geometric characteristics of the harmonic evolute surfaces of tubular surfaces. The characterizations of the harmonic evolute surface’s ϱ and ς parameter curves are evaluated, and then, they are compared. Finally, an example of a tubular surface’s harmonic evolute surface is presented, along with visuals of these surfaces.

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