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Author : E.M. Solouma
Publisher : Infinite Study
Page : 7 pages
File Size : 53,5 Mb
Release : 2024-07-01
Category : Electronic
ISBN : 8210379456XXX
In this paper, we introduce special equiform Smarandache curves reference to the equiform Frenet frame of a curve on a spacelike surface M in Minkowski 3-space E31.
Author : Melih Turgut , Suha Yilmaz
Publisher : Infinite Study
Page : 5 pages
File Size : 42,5 Mb
Release : 2024-07-01
Category : Electronic
ISBN : 8210379456XXX
A regular curve in Minkowski space-time, whose position vector is composed by Frenet frame vectors on another regular curve, is called a Smarandache Curve.
Author : E. M. Solouma, W. M. Mahmoud
Publisher : Infinite Study
Page : 17 pages
File Size : 55,5 Mb
Release : 2024-07-01
Category : Mathematics
ISBN : 8210379456XXX
In this paper, we introduce the equiform-Bishop frame of a spacelike curve r lying fully on S21 in Minkowski 3-space R31. By using this frame, we investigate the equiform-Bishop Frenet invariants of special spacelike equiform-Bishop Smarandache curves of a spacelike base curve in R31 . Furthermore, we study the geometric properties of these curves when the spacelike base curve r is specially contained in a plane. Finally, we givea computational example to illustrate these curves.
Author : Emad Solouma
Publisher : Infinite Study
Page : 14 pages
File Size : 44,8 Mb
Release : 2023-01-01
Category : Mathematics
ISBN : 8210379456XXX
In this paper, some geometric properties of equiform Smarandache ruled surfaces in Minkowski space E13 using an equiform frame are investigated. Also, we give the sufficient conditions that make these surfaces are equiform developable and equiform minimal related to the equiform curvatures and when the equiform base curve contained in a plane or general helix. Finally, we provide an example, such as these surfaces.
Author : Emad Solouma
Publisher : Infinite Study
Page : 17 pages
File Size : 53,8 Mb
Release : 2024-07-01
Category : Mathematics
ISBN : 8210379456XXX
In this paper, we construct the equiform spacelike Smarandache curves of spacelike anti-equiform Salkowski curves with timelike binormal according to equiform frame. Furthermore, we calculate the equiform Frenet apparatus of these curves. Finally, the latter curves were plotted.
Author : E. M. Solouma,M. M. Wageeda
Publisher : Infinite Study
Page : 9 pages
File Size : 47,6 Mb
Release : 2024-07-01
Category : Electronic
ISBN : 8210379456XXX
In this paper, we introduce some special Smarandache curves according to Bishop frame in Euclidean 3-space E3.
Author : Emad Solouma,Ibrahim Al-Dayel,Meraj Ali Khan,Mohamed Abdelkawy
Publisher : Infinite Study
Page : 19 pages
File Size : 48,8 Mb
Release : 2024-01-01
Category : Mathematics
ISBN : 8210379456XXX
This study begins with the construction of type-Π Smarandache ruled surfaces, whose base curves are Smarandache curves derived by rotation-minimizing Darboux frame vectors of the curve in E3. The direction vectors of these surfaces are unit vectors that convert Smarandache curves. The Gaussian and mean curvatures of the generated ruled surfaces are then separately calculated, and the surfaces are required to be minimal or developable. We report our main conclusions in terms of the angle between normal vectors and the relationship between normal curvature and geodesic curvature. For every surface, examples are provided, and the graphs of these surfaces are produced.
Author : H.S. Abdel-Aziz,M. Khalifa Saad
Publisher : Infinite Study
Page : 9 pages
File Size : 43,9 Mb
Release : 2024-07-01
Category : Mathematics
ISBN : 8210379456XXX
In this paper, we study Smarandache curves according to Darboux frame in the three-dimensional Minkowski space. Using the usual transformation between Frenet and Darboux frames, we investi- gate some special Smarandache curves for a given timelike curve lying fully on a timelike surface. Finally, we defray a computational example to confirm our main results.
Author : Stuti Tamta,Ram Shankar Gupta
Publisher : Infinite Study
Page : 19 pages
File Size : 49,9 Mb
Release : 2023-01-01
Category : Mathematics
ISBN : 8210379456XXX
In this paper, we study the developable TN, TB, and NB-Smarandache ruled surface with a pointwise 1-type Gauss map. In particular, we obtain that every developable TN-Smarandache ruled surface has constant mean curvature, and every developable TB-Smarandache ruled surface is minimal if and only if the curve is a place curve with non-zero curvature or a helix, and every developable NB-Smarandache ruled surface is always plane. We also provide some examples.
Author : Esra Betul Koc Ozturk, Ufuk Ozturk, Kazim Ilarslan,Emilija Nešovi
Publisher : Infinite Study
Page : 15 pages
File Size : 47,9 Mb
Release : 2024-07-01
Category : Electronic
ISBN : 8210379456XXX
In this paper we define nonnull and nullpseudospherical Smarandache curves according to the Sabban frame of a spacelike curve lying on pseudosphere in Minkowski 3-space.
Author : H.S.Abdel-Aziz ,M.Khalifa Saad
Publisher : Infinite Study
Page : 13 pages
File Size : 50,7 Mb
Release : 2024-07-01
Category : Electronic
ISBN : 8210379456XXX
In the present paper, Smarandache curves for some special curves in the threedimensional Galilean space G3are investigated. Moreover, spherical indicatrices for the helix as well as circular helix are introduced. Furthermore, some properties for these curves are given. Finally, in the light of this study, some related examples of these curves are provided.
Author : Tanju Kahraman
Publisher : Infinite Study
Page : 6 pages
File Size : 40,9 Mb
Release : 2024-07-01
Category : Electronic
ISBN : 8210379456XXX
In this paper, we define Smarandache curves of null quaternionic curves in the semi-Euclidean space 31E and obtaine that curvatures of null quaternionic curves have some relations for Smarandache curves.
Author : Tanju Kahraman,Hasan Hüseyin Uğurlu
Publisher : Infinite Study
Page : 13 pages
File Size : 46,7 Mb
Release : 2024-07-01
Category : Mathematics
ISBN : 8210379456XXX
In this paper, we give Darboux approximation for dual Smarandache curves of spacelike curve on unit dual Lorentzian sphere.
Author : Tanju Kahraman,Hasan Huseyin Ugurlu
Publisher : Infinite Study
Page : 9 pages
File Size : 55,9 Mb
Release : 2024-07-01
Category : Electronic
ISBN : 8210379456XXX
In this paper, we consider the notion of the Smarandache curves by considering the asymptotic orthonormal frames of curves lying fully on lightlike cone in Minkowski 3- space R3 1. We give the relationships between Smarandache curves and curves lying on lightlike cone in R31.
Author : M. Khalifa Saad
Publisher : Infinite Study
Page : 8 pages
File Size : 48,9 Mb
Release : 2024-07-01
Category : Mathematics
ISBN : 8210379456XXX
In this paper, we study space and timelike admissible Smarandache curves in the pseudo-Galilean space. Also, we obtain Smarandache curves of the position vector of space and timelike arbitrary curve with some of its special curves. Finally, we defray and illustrate some examples to confirm our main results.