# THE FUNDAMENTAL FORMULAS OF FINSLER SUBMANIFOLDS

• Li, Jintang
• Published : 2010.07.31
• 56 6

#### 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

#### References

1. D. Bao and S. S. Chern, On a notable connection in Finsler geometry, Houston J. Math. 19 (1993), no. 1, 135–180.
2. D. Bao, S. S. Chern, and Z. Shen, An Introduction to Riemann-Finsler Geometry, Graduate Texts in Mathematics, 200. Springer-Verlag, New York, 2000.
3. A. Bejancu, Structure equations for Riemann-Finsler subspaces, C. R. Acad. Bulgare Sci. 40 (1987), no. 1, 37–40.
4. Z. Shen, On Finsler geometry of submanifolds, Math. Ann. 311 (1998), no. 3, 549–576. https://doi.org/10.1007/s002080050200

#### Cited by

1. The pinching theorem for hypersurfaces of Minkowski spaces vol.388, pp.2, 2012, https://doi.org/10.1016/j.jmaa.2011.11.022