Essin Turhan

Characterize on the Heisenberg group with left invariant Lorentzian metric

In this paper, we consider the biharmonicity conditions for maps between Riemannian manifolds and we characterize non-geodesic biharmonic curve in Heisenberg group Hz which is endowed with left invariant Lorentzian metric.

Time Evolution Equations for Surfaces Generated via Binormal Spherical Image in Terms of Inextensible Flows in

Abstract In this work, we study time-evolution equations that the intrinsic quantities of curves to construct binormal spherical curves as surfaces in terms of inextensible flows in . Using the Frenet frame of the given curve, we present partial differential equations. We give necessary and sufficient condition for a binormal spherical curves as surfaces to be a Bonnet surface. Finally, we draw some pictures of our main results.

Inextensible flows of biharmonic S-curves according to Sabban frame in Heisenberg group Heis3

Abstract In this work, we examine inextensible flows associated biharmonic curves depending to Sabban frame in Heis3. We define the biharmonic curves with regards to their curvatures. The differential equations characterizing biharmonic curves are given in Heis3. Additionaly, we discover equations of one parameter family of biharmonic curves in .

Asymptotic curves on B-surfaces according to type-2 bishop frame in the sol space

Abstract In this paper, we study B— surfaces of biharmonic constant Π2— slope curves according to type-2 Bishop in the . We characterize asymptotic curves on B— surfaces of biharmonic constant Π2— slope curves in terms of their Bishop curvatures. Finally, we find out their explicit parametric equations in the .

TANGENT SURFACES OF BIHARMONIC B-GENERAL HELICES ACCORDING TO BISHOP FRAME IN HEISENBERG GROUP Heis 3

In this paper, we study tangent surfaces of biharmonic B-general helices according to Bishop frame in the Heisenberg group Heis 3 . We give necessary and sufficient conditions for B-general helices to be biharmonic according to Bishop frame. We characterize the tangent surfaces of biharmonic B-general helices in terms of Bishop frame in the Heisenberg group Heis 3 . Additionally, we illustrate our main theorem.

On Inextensible Flows of Curves According toType-2 Bishop Frame in E3

In this paper, we study inextensible flows of curves in Euclidean space 3 E . Using the Frenet frame of the given curve, we present partial differential equations. We give some characterizations for curvatures of a curve in Euclidean space . 3 E

On Timelike Biharmonic General Helices in the Lorentzian E ( 1 ,1 )

In this paper, we study timelike biharmonic general helices in the Lorentzian group of rigid motions (1,1) E . We characterize the timelike biharmonic general helices in terms of their curvature and torsion in the Lorentzian group of rigid motions (1,1) E .

Construction of Focal Curves of Spacelike 0-Biharmonic Curves with Timelike Binormal in the Lorentzian Heisenberg Group Heis3

In this paper, we study focal curve of spacelike biharmonic curve with a timelike binormal in the Heis 3 . We characterize focal curve of spacelike biharmonic curve with a timelike binormal in terms of curvature and torsion of biharmonic curve in the Heis . 3 Finally, we construct parametric equations of focal curve of spacelike biharmonic curve with a timelike binormal curve.

Solutions of Differential Equations for Dual Curvatures of Dual Biharmonic Curves with Spacelike Principal Normal in D31

In this paper, we study dual spacelike biharmonic curves with spacelike principal normal for dual variable in dual Lorentzian space . 3 1 D We consider differential equations of dual Bishop curvatures of dual spacelike biharmonic curves with spacelike principal normal for dual variable in dual Lorentzian space 3 1 D . This equations are seperated into dual and real parts such that the dual part of the equation is the higher order differential of each term in the real part.

A New Characterization of Smarandache Tsα Curves According to Sabban Frame in Heisenberg Group Heis

In this paper, we study Smarandache tsα curves according to Sabban frame in the Heisenberg group Heis 3 . Finally, we find explicit parametric equations of Smarandache tsα curves according to Sabban Frame.