Biharmonic maps from Finsler spaces

TL;DR

This paper extends the concepts of bienergy and biharmonic maps from Riemannian to Finsler spaces, deriving variation formulas, equations, and examples, and generalizes key Riemannian results to Finsler geometry.

Contribution

It introduces the notion of biharmonic maps from Finsler spaces, deriving their variational formulas and equations, and extends classical Riemannian results to the Finsler setting.

Findings

Derived first and second variation formulas for bienergy in Finsler spaces

Established equations for Finsler-to-Riemann biharmonic maps

Extended nonexistence results of nonharmonic biharmonic maps to Finsler geometry

Abstract

The notions of bienergy of a smooth mapping and of biharmonic map between Riemannian manifolds are extended to the case when the domain is Finslerian. We determine the first and the second variation of the bienergy functional, the equations of Finsler-to-Riemann biharmonic maps and some specific examples. Two notable results in Riemannian geometry concerning the inexistence of nonharmonic biharmonic maps are extended without difficulty in our case.