Journal of the
Korean Mathematical Society JKMS

Biharmonic curves are a generalization of geodesics, with applications in elasticity theory and 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, specific properties and existence of non-geodesic biharmonic curves for some classes of Finsler spaces. Integration of the biharmonic equation is presented for two concrete Finsler metrics.

Keywords: Finsler space, bienergy, biharmonic curve

MSC numbers: 53B40, 53C60, 31B30, 58E10