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

Abstract

In this paper, we study f-biharmonic Legendre curves in S-space forms. Our aim is to find curvature conditions for these curves and determine their types, i.e., a geodesic, a circle, a helix or a Frenet curve of osculating order r with specific curvature equations. We also give a proper example of f-biharmonic Legendre curves in the S-space form R 2m+s (−3s), with m = 2 and s = 2.

On Bi-f-Harmonic Legendre Curves in Sasakian Space Forms

“…The sectional curvature of a φ -section is called φsectional curvature such that a S -manifold of constant φ -section curvature c is called as S -space form. Finally, if s = 1 , a S -space form becomes a Sasakian space form [2,6,7]. For a SSF, from equations ( 6) and (7), it is easy to see that…”

“…Definition 2.1 A Legendre curve of a SSF (N 2n+1 , φ, ξ, η, g) is a one dimensional integral submanifold of N and β ∶ I → (N 2n+1 , φ, ξ, η, g) is a Legendre curve if η(T ) = 0 , where T is the tangent vector field of β [6,7].…”