  In this short paper, we study a symmetric covariant tensor in Finsler
geometry, which is called the mean Berwald curvature. We first investigate the
geometry of the fibres as the submanifolds of the tangent sphere bundle on a
Finsler manifold. Then we prove that if the mean Berwald curvature is isotropic
along fibres, then the Berwald scalar curvature is constant along fibres.

Differential Geometry