New Examples of $F$-planar Curves in 3-dimensional Warped Product Manifolds

Ana Irina Nistor

The notion of $F$-planar curves generalizes the magnetic curves and implicitly the geodesics. In this note we obtain all $F$-planar curves in the Euclidean space ${\mathbb{E}}^3$ with constant coefficients and we prove that they are generalized helices. We give a detailed study for $F$-planar curves in the warped product ${\mathbb{R}}\times_f{\mathbb{R}}^2$.