Biharmonic curves in Finsler spaces

Abstract

Biharmonic curves are a generalization of geodesics, with applications in elasticity theory and various branches of computer science. The paper proposes a first study of biharmonic curves in spaces with Finslerian geometry, covering the following topics: a deduction of their equations, existence of non-geodesic biharmonic curves for some classes of Finsler spaces and specific properties. We prove, for instance, that geodesic curvature is constant along Finslerian biharmonic curves. Integration of the biharmonic equation is presented for two concrete Finsler metrics.