THEORY OF FINSLER SUBMANIFOLDS VIA BERWALD CONNECTION

Abstract

Let Fm = (M;F ) be a Finsler submanifold of a Finsler manifold em+p = (f M; e F ). By using the normal curvature vector eld of Fm and the Berwald connections on both F m and e m+p , we obtain the structure equations for the immersion of F m into e m+p . This enables us to relate, for the rst time in literature, the ag curvatures of F m and e m+p . Finally, we investigate the existence of totally geodesic Finsler submanifolds of a Randers (c;K)-sphere.