The variation formulas of Finsler submanifolds

Let φ:(Mn,F)→(M¯n+p,F¯) be an isometric immersion from a Finsler manifold to a Finsler manifold. In this paper, we establish the first variation formula of volume in terms of the Chern connection of MM. We also determine the second variation formula of volume for the Landsberg hypersurfaces in Minkowski spaces.