Bulletin of the
Korean Mathematical Society BKMS

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 $\overline{M}$.

Keywords: Finsler submanifolds, Gauss equation, weakly totally geodesic

MSC numbers: 53C60, 53C40