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.