THE FUNDAMENTAL FORMULAS OF FINSLER SUBMANIFOLDS

Let ${\varphi}\;:\;(M^n,\;F)\;{\rightarrow}\;(\overline{M}^{n+p},\;\overline{F})$ be an isometric immersion from a Finsler manifold to a Finsler manifold. In this paper, we shall obtain the Gauss and Codazzi equations with respect to the Chern connection on submanifolds M, by which we prove that if M is a weakly totally geodesic submanifold of $\overline{M}$, then flag curvature of M equals flag curvature of $\overline{M}$.