On the classification of Landsberg spherically symmetric Finsler metrics

In this paper, as an application of the inverse problem calculus variations, we investigate two compatibility conditions on spherically symmetric Finsler metrics. By making use these conditions, focus our attention Landsberg We classify all manifolds or Berwald types. For higher dimensions $n\geq 3$, prove that: are either Riemannian their geodesic sprays have a specific formula; regular metrics Riemannian; (regular non-regular) Riemannian. Moreover, establish new unicorns, i.e., explicit examples non-regular non-Berwaldian obtained. two-dimensional case, characterize surfaces.