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 The fundamental formulas of Finsler submanifolds Bull. Korean Math. Soc. 2010 Vol. 47, No. 4, 767-775 https://doi.org/10.4134/BKMS.2010.47.4.767Published online July 1, 2010 Jintang Li Xiamen University Abstract : 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 Full-Text :