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THE FUNDAMENTAL FORMULAS OF FINSLER SUBMANIFOLDS

  • Li, Jintang
  • Received : 2009.02.13
  • Published : 2010.07.31

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

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  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