Biharmonic Legendre Curves in Sasakian Space Forms

On Biharmonic Legendre curves in $S$-space forms

“…In [12] and [14], Fetcu and Oniciuc studied biharmonic Legendre curves in Sasakian space forms. As a generalization of their studies, in the present paper, we study biharmonic Legendre curves in S− space forms.…”

“…Biharmonic submanifolds have been studied by many geometers. For example, see [2], [3], [7], [8], [11], [12], [13], [14], [15], [18], [20], [21], [22], and the references therein. In a different setting, in [9], Chen defined a biharmonic submanifold M ⊂ E n of the Euclidean space as its mean curvature vector field H satisfies ∆H = 0 , where ∆ is the Laplacian.…”

Slant and Legendre curves in Bianchi-Cartan-Vranceanu geometry

“…1) the rôle of Legendre curves in almost contact geometry is remarkable and wellknown; in [4] the reader finds an excellent survey on these curves, 2) although the literature on Legendre curves is rich ( [3], [5], [7], [16], [20], [24], [25]), slant curves have been studied until now only for the Sasakian geometry in [12], for the contact pseudo-Hermitian geometry in [14], for the f -Kenmotsu geometry in [10], in normal almost contact geometry in [8] and for warped products in [9]. Although some Bianchi-Cartan-Vranceanu metrics are almost contact metrics we prefer in the present work a unified treatment in order to emphasize the common properties of these metrics.…”

Curvature and torsion of a legendre curve in (e;d) Trans-Sasakian manifolds

“…Since any harmonic maps is biharmonic, we are interested in proper biharmonic maps, that is non-harmonic biharmonic maps. Biharmonic maps have been studied intensively in the last decade (see [7], [8], [9], [24], [25], [26], [2], [19], [20], [21]). In the study of almost contact manifolds, Legendre curves play an important role, e. g., a diffeomorphism of a contact manifold is a contact transformation if and only if it maps Legendre curve to Legendre curve.…”