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

We consider f-biharmonic Legendre curves in Sasakian space forms. We find curvature characterizations of these types of curves in four cases.

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In this paper, we study normal magnetic curves in C-manifolds. We prove that magnetic trajectories with respect to the contact magnetic fields are indeed θα-slant curves with certain curvature functions. Then, we give the parametrizations of normal magnetic curves in R 2n+s with its structures as a C-manifold.

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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.

In this study, we consider curves of generalized AW (k)-type of Euclidean n-space. We give curvature conditions of these kind of curves.Mathematics Subject Classification. 53C40, 53C42.

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