Electronic Journal of Theoretical Physics Involute Curves Of Timelike Biharmonic Reeb Curves (LCS)3- Manifolds (original) (raw)

Involute Curves Of Timelike Biharmonic Reeb Curves (LCS)3-Manifolds

Electronic Journal of Theoretical Physics, 2012

In this paper, we study involute timelike biharmonic Reeb curves in (LCS) 3manifold. We characterize curvatures of timelike biharmonic Reeb curves in (LCS) 3-manifold. We obtain parametric equation involute curves of the timelike biharmonic Reeb curves in (LCS) 3-manifold.

Biharmonic Curves in a Strict Walker 3-Manifold

Int. J. Math. Math. Sci., 2022

In this paper, we study the geometry of biharmonic curves in a strict Walker 3-manifold and we obtain explicit parametric equations for biharmonic curves and time-like biharmonic curves, respectively. We discuss the conditions for a speed curve to be a slant helix in a Walker manifold. We give an example of biharmonic curve for illustrating the main result.

Some new notes on the involutes of the timelike curves in Minkowski 3-space

C. Huygens, who is also known for his works in optics, discovered involutes while trying to build a more accurate clock. The involute of a given curve is a well-known concept in the Euclidean space (see ,[4], [5], [8]). In [2], authors have defined the involutes of the timelike curve α in Minkowski 3-space and showed that the lenght between the timelike curve α and the space like curve β is constant. Furthermore, the curvature and the torsion of the involute curves β have been found as depend on the curvature and the torsion of the evolute curve α. In this paper, we have found the relationships between the Frenet frames of the timelike curve α and the spacelike involute curve β and some new characterizations with relation to the involute-evolute curve couple (β, α) have been found. Finally, we have given one example of the involutes of the timelike curve.

On characterization bertrand mate of timelike biharmonic curves in the lorentzian Heis3

Revista Notas de Matemática Vol.7(1),No. 307, 2011, pp. 84-91 http://www.saber.ula.ve/notasdematematica Comisión de Publicaciones Departamento de Matemáticas Facultad de Ciencias Universidad de Los Andes ... ON CHARACTERIZATION BERTRAND MATE OF TIMELIKE BIHARMONIC CURVES IN THE LORENTZIAN Heis3 ... Talat Körpınar, Essin Turhan, Iqbal H. Jebril ... In this paper, we study non-geodesic timelike biharmonic curves and we construct parametric equations for Bertrand mate of timelike biharmonic curves in the Lorentzian Heisenberg group Heis

Todjihounde: Biharmonic Reeb curves in Sasakian manifolds

2016

Sasakian manifolds provide explicit formulae of some Jacobi operators which describe the biharmonic equation of curves in Riemannian manifolds. In this paper we characterize non-geodesic biharmonic curves in Sasakian manifolds which are either tangent or normal to the Reeb vector field. In the three-dimensional case, we prove that such curves are some helixes whose geodesic curvature and geodesic torsion satisfy a given relation.

Biharmonic Reeb Curves in Sasakian Manifolds

arXiv: Differential Geometry, 2010

Sasakian manifolds provide explicit formulae of some Jacobi opera- tors which describe the biharmonic equation of curves in Riemannian manifolds. In this paper we characterize non-geodesic biharmonic curves in Sasakian mani- folds which are either tangent or normal to the Reeb vector field. In the three-dimensional case, we prove that such curves are some helixes whose geodesic curvature and geodesic torsion satisfy a given relation.