Concircular Transformations on Isotropic Finsler Manifolds

Concircular Transformations on Isotropic Finsler Manifolds

Here, it is shown that if a forward geodesically complete Finsler manifold (M; F) admits a concircular change of metric, then the indicatrix is conformally dieomorphic to the standard (n-1)-sphere in the Euclidean space Rn. Moreover, it is proved that every forward geodesically complete absolutely homogeneous isotropic Finsler manifold which admits a concircular change of metric is a Riemannian manifold of constant sectional curvature.