On Biharmonic Legendre curves in $S$-space forms

Abstract

We study biharmonic Legendre curves in S− space forms. We find curvature characterizations of these special curves in 4 cases.

On the characterizations of f-biharmonic legendre curves in Sasakian space forms

“…which has the general solution (12) under the condition c 3 < −2 (1 + c 2 2 ). (13) must be also satisfied.…”

“…D. Fetcu and C. Oniciuc studied biharmonic Legendre curves in Sasakian space forms in [6] and [7]. We studied biharmonic Legendre curves in generalized Sasakian space forms and S-space forms in [13] and [12], respectively. In the present paper, we consider f -biharmonic Legendre curves in Sasakian space forms.…”

A Note on f-biharmonic Legendre Curves in S-Space Forms

“…Hence γ cannot be proper f -biharmonic. Previously, in [19], we claimed that γ cannot be proper biharmonic either.…”

C-parallel and C-proper slant curves of S-manifolds

“…for all α = 1, ..., s, then γ is called a Legendre curve of M [21]. More generally, if there exists a constant angle θ such that η α (T ) = cos θ, for all α = 1, ..., s, then γ is called a slant curve and θ is called the contact angle of γ, where |cos θ| ≤ 1/ √ s [12].…”

“…Calvaruso, Munteanu and Perrone provided a complete classification of the magnetic trajectories of a Killing characteristic vector field on an arbitrary normal paracontact metric manifold of dimension 3 in [7]. The present authors considered biharmonic Legendre curves of S-space forms in [21]. The second author studied magnetic curves in the 3-dimensional Heisenberg group in [22].…”