Integral formulae for codimension-one foliated Finsler manifolds

We study extrinsic geometry of a codimension-one foliation F of a Finsler space (M; F), in particular, of a Randers space (M; α + β). Using a unit vector field ν orthogonal (in the Finsler sense) to the leaves of F, we define a new Riemannian metric g on M, which for Randers case depends nicely on (α; β). For that g we derive several geometric invariants of F (e.g. the Riemann curvature and the shape operator) in terms of F; then under natural assumptions on β which simplify derivations, we express them in terms of invariants arising from α and β. Using our approach of [13], we produce the integral formulae for F of closed (M; F) and (M; α + β), which relate integrals of mean curvatures with those involving algebraic invariants obtained from the shape operator of F and the Riemann curvature in the direction ν. They generalize formulae by Brito-Langevin-Rosenberg (that total mean curvatures of any order for a foliated closed Riemannian space of constant curvature don't depend on a choice of F).