Biharmonic Curves in a Strict Walker 3-Manifold (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 timelike curves according to Bishop frame in Minkowski 4-space

2018

In the last decade there has been a growing interest in the theory of biharmonic maps which can be divided in two main research directions. On the one side, constructing the examples and classification results has become important from the differential geometric aspect. The other side is the analytic aspect from the point of view of partial differential equations, because biharmonic maps are solutions of a fourth order strongly elliptic semi linear PDE.Biharmonic curves γ : I ?⊂???→(N, h) of a Riemannian manifold are the solutions of the fourth order differential equation 3 R( , 3 ) 0, γ γ γ γ γ γ ′ ′ ∇ ′ − ′ ∇ ′ ′ = (1) where,∇ is the Levi-Civita connection on (N, h) and R is its curvature operator. As we shall detail in the next section, they arise from a variational problem and are a natural generalization of geodesics. In the last decade biharmonic curves have been extensively studied and classified in several spaces by analytical inspection of Equation 1 [1-15].Although much wo...

Biharmonic curves on LP-Sasakian manifolds

2008

In this paper we give necessary and sufficient conditions for spacelike and timelike curves in a conformally flat, quasi conformally flat and conformally symmetric 4-dimensional LP-Sasakian manifold to be proper biharmonic. Also, we investigate proper biharmonic curves in the Lorentzian sphere S^4_1.

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.