Harmonic Finsler manifolds of $({\alpha}, \beta)$-type

TL;DR

This paper introduces a new class of harmonic Finsler manifolds of $({\alpha},\beta)$-type, constructed using a Riemannian metric and a special 1-form, expanding the understanding of harmonic structures in Finsler geometry.

Contribution

The paper constructs a novel class of harmonic and asymptotically harmonic Finsler manifolds of $({\alpha},\beta)$-type, based on specific Riemannian metrics and 1-forms, advancing Finsler geometric theory.

Findings

Defined a new class of harmonic Finsler manifolds

Established conditions for asymptotic harmonicity

Expanded the class of known harmonic Finsler structures

Abstract

In this paper we construct a new class of harmonic and asymptotically harmonic Finsler manifolds of $({\alpha},\beta)$-type. This class is defined by a Riemannian metric ${\alpha}$ and a special 1-form $\beta$.