Mannheim curves with modified orthogonal frame in Euclidean 3-space

Lone, M. S.; Es, Hasan; Karacan, Murat Kemal; Bükcü, Bahaddin

doi:10.3906/mat-1807-177

Cited by 14 publications

(6 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They gave a condition for a given curve to be a Mannheim curve. Also, [6]- [9] can be looked at for examining Bertand and Mannheim curves in different spaces. Recently, C ¸.…”

Section: Introductionmentioning

confidence: 99%

Generalized Bertrand and Mannheim Curves in 3D Lie Groups

Okuyucu

Yazıcı

2022

Fundamental Journal of Mathematics and Applications

View full text Add to dashboard Cite

show abstract

“…They gave a condition for a given curve to be a Mannheim curve. Also, [6]- [9] can be looked at for examining Bertand and Mannheim curves in different spaces. Recently, C ¸.…”

Section: Introductionmentioning

confidence: 99%

Generalized Bertrand and Mannheim Curves in 3D Lie Groups

Okuyucu

Yazıcı

2022

Fundamental Journal of Mathematics and Applications

View full text Add to dashboard Cite

show abstract

“…Additionally, some characteristic features of this surfaces have been obtained and visual applications related to modified orthogonal rollar coaster surface and its parallel surface have been given [14]. Lone et al have defined Mannheim pairs, Frenet-Mannheim curves and weakened Mannheim curves according to modified orthogonal frame in the Euclidean 3-space and obtained some characterizations of these www.josa.ro Mathematics Section curves [15]. Later, Lone et al have studied helices and the Bertrand curves according to modified orthogonal frame in the Euclidean 3-space.…”

Section: Introductionmentioning

confidence: 99%

Involute-Evolute Curves According to Modified Orthogonal Frame

Azak

2021

J. Sci. Arts

View full text Add to dashboard Cite

In this paper, the involute-evolute curve concept has been deﬁned according to two type modiﬁed orthogonal frames at non-zero points of curvature and torsion in the Euclidean space E^3 , respectively. Later, the characteristic theorems related to the distance between the corresponding points of these curves have been given. Besides, the relations have been found between the curvatures and also torsions of the two type the involute-evolute modiﬁed orthogonal pairs.

show abstract

“…There is a very close relation between this frame and Serret-Frenet frame. In the literature, there have been numerous studies about the Modified orthogonal frame [11,12,13,14,15]. In this paper, firstly, we have given a short knowledge about the Serret-Frenet frame and modified orthogonal frame.…”

Section: Introductionmentioning

confidence: 99%

A Note on the Acceleration and Jerk in Motion Along a Space Curve

Özen¹,

Güner

Tosun

2020

Analele Universitatii "Ovidius" Constanta - Seria Matematica

View full text Add to dashboard Cite

The resolution of the acceleration vector of a particle moving along a space curve is well known thanks to Siacci [1]. This resolution comprises two special oblique components which lie in the osculating plane of the curve. The jerk is the time derivative of acceleration vector. For the jerk vector of the aforementioned particle, a similar resolution is presented as a new contribution to field [2]. It comprises three special oblique components which lie in the osculating and rectifying planes. In this paper, we have studied the Siacci’s resolution of the acceleration vector and aforementioned resolution of the jerk vector for the space curves which are equipped with the modified orthogonal frame. Moreover, we have given some illustrative examples to show how the our theorems work.

show abstract

Mannheim curves with modified orthogonal frame in Euclidean 3-space

Abstract: In this paper, we investigate Mannheim pairs, Frenet-Mannheim curves and Weakened Mannheim curves with respect to the modified orthogonal frame in Euclidean 3-space(E 3 ). We obtain some characterizations of these curves.2000 Mathematics Subject Classification. 53A04, 53A35.

Cited by 14 publications

References 6 publications

Generalized Bertrand and Mannheim Curves in 3D Lie Groups

Generalized Bertrand and Mannheim Curves in 3D Lie Groups

Involute-Evolute Curves According to Modified Orthogonal Frame

A Note on the Acceleration and Jerk in Motion Along a Space Curve

Contact Info

Product

Resources

About