Browsing by Author "0000000210282676 [Şimşek, Hakan]"
Now showing items 19 of 9

Bäcklund’s theorem for n dimensional lorentzian submanifold in the minkowski space 𝔼21𝑛−1
Şimşek, Hakan; Özdemir, Mustafa (Results in Mathematics, 2016)In this paper, Bäcklund’s Theorem is introduced on the Lorentzian nsubmanifold of the Minkowski space 𝔼2𝑛−11 by using the method of moving frames. Also, we prove the Integrability Theorem for the Lorentzian nsubmanifold ... 
Generating hyperbolical rotation matrix for a given hyperboloid
Şimşek, Hakan; Özdemir, Mustafa (Linear Algebra and Its Applications, 2016)Hyperbolic rotation is hyperbolically the motion of a smooth object on general hyperboloids given by −a1x2+a2y2+a3z2=±λ, λ ∈R+. In this paper, we investigate the hyperbolical rotation matrices in order to get the motion ... 
On conformal curves in 2dimensional de sitter space
Şimşek, Hakan; Özdemir, Mustafa (Advances in Applied Clifford Algebras, 2016)In this paper, we examine the pseudospherical curves, which are equivalent to each other under the conformal maps preserving a fixed point in the de Sitter 2space, by using the Clifford algebra Cl 2,1. Also, we find the ... 
On focal curves of null Cartan curves
Şimşek, Hakan (Turkish Journal of Mathematics, 2017)The focal curve, which is determined as the locus of centers of osculating pseudospheres of a null Cartan curve, is investigated in Minkowski (n+2)space Mn+2. Moreover, a curve called acceleration focal curve of a null ... 
On the eigenvalues and eigenvectors of a lorentzian rotation matrix by using split quaternions
Özdemir, Mustafa; Erdoğdu, Melek; Şimşek, Hakan (Advances in Applied Clifford Algebras, 2014)In this paper, we examine eigenvalue problem of a rotation matrix in Minkowski 3 space by using split quaternions. We express the eigenvalues and the eigenvectors of a rotation matrix in term of the coefficients of the ... 
Rotations on a lightcone in minkowski 3Space
Şimşek, Hakan; Özdemir, Mustafa (Advances in Applied Clifford Algebras, Springer, 2017)In this paper the generalization of the rotations on any lightcone in Minkowski 3space ℝ1,2𝑔 is given. The rotation motion on the lightcone is examined by means of a bilinear form and Lorentzian notions. We use the ... 
Shape curvatures of the Lorentzian plane curves
Şimşek, Hakan; Özdemir, Mustafa (Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 2017)In this paper, we examine the Lorentzian similar plane curvesusing the hyperbolic structure and spherical arc length parameter. We classifyall selfsimilar Lorentzian plane curves and give formulas for pseudo shapecurvatures ... 
Similar and selfsimilar curves in minkowski nspace
Şimşek, Hakan; Özdemir, Mustafa (Bulletin of Korean Mathematical Society, 2015)In this paper, we investigate the similarity transformations in the Minkowski nspace. We study the geometric invariants of nonnull curves under the similarity transformations. Besides, we extend the fundamental theorem ... 
Some results on pshape curvatures of nonlightlike space curves
Şimşek, Hakan; Özdemir, Mustafa (International Electronic Journal of Geometry, 2018)In this paper, we obtain some findings for a nonnull curve parameterized by spherical arc length. We investigate the relationship between a nonnull curve with pshape curvatures and pseudospherical curves on S21 and ...