Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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THE FUNDAMENTAL FORMULAS OF FINSLER SUBMANIFOLDS

  • Li, Jintang (DEPARTMENT OF MATHEMATICS XIAMEN UNIVERSITY)
  • Received : 2009.02.13
  • Published : 2010.07.31
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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 $\overline{M}$.

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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

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