THE FUNDAMENTAL FORMULAS OF FINSLER SUBMANIFOLDS

Title & Authors
THE FUNDAMENTAL FORMULAS OF FINSLER SUBMANIFOLDS
Li, Jintang;

Abstract
Let $\small{{\varphi}\;:\;(M^n,\;F)\;{\rightarrow}\;(\overline{M}^{n+p},\;\overline{F})}$ 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 $\small{\overline{M}}$, then flag curvature of M equals flag curvature of $\small{\overline{M}}$.
Keywords
Finsler submanifolds;Gauss equation;weakly totally geodesic;
Language
English
Cited by
1.
The pinching theorem for hypersurfaces of Minkowski spaces, Journal of Mathematical Analysis and Applications, 2012, 388, 2, 1285
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