Biharmonic curves along Riemannian submersions

The purpose of this paper is to study biharmonic curves along Riemannian submersions. We first consider a Riemannian submersion from a Riemannian manifold onto Riemannian manifold and investigate under what conditions a biharmonic curve on the total manifold is transformed to a biharmonic curve on the base manifold. We obtain several results with certain restrictions on curvatures. We then consider a Riemannian submersion from a Kaehler manifold onto a Riemannian manifold. Necessary and sufficient conditions were obtained for a curve that is biharmonic in the total manifold of Riemannian submersion to be biharmonic on the base manifold along the Riemannian submersion. In addition, considering the special cases of the curvatures of the curve, the biharmonicity of the curve on the base manifold is discussed.