Biharmonic curves in Finsler spaces

TL;DR

This paper introduces and studies biharmonic curves within Finsler spaces, deriving their equations, exploring their existence beyond geodesics, and analyzing their properties in specific Finsler geometries.

Contribution

It is the first to analyze biharmonic curves in Finsler spaces, including their equations, existence, and properties, expanding the understanding of such curves in generalized geometries.

Findings

Existence of non-geodesic biharmonic curves in some Finsler spaces

Constant geodesic curvature along biharmonic curves

Explicit integration of biharmonic equations for specific Finsler metrics

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.