Advertisement

Some cross-section theorems on the tangent bundle over a finslerian manifold

  • 32 Accesses

  • 1 Citations

Summary

Let T(M) be the tangent bundle over a Finslerian manifold M of n-dimension endowed with the Cartan connection ∇. One makes T(M) into a 2n dimensional affinely connected manifold by assigning a connection ∇c to T(M). The cross-section\(\mathfrak{B}\) of a vector field V defined in M reveals in T(M) an n-dimensional submanifold and its geometry is developed by means of the affine subspace theory and of the affine collineations in the base Finsler manifold.

References

  1. [1]

    T. Okubo,Cross-section theorems on the tangent bundle over a generalized space of paths, to appear in Revue Roumaine Math. pures et applic.

  2. [2]

    H. Rund,The differential geometry of Finsler spaces, Springer-Verlag, Berlin, 1959.

  3. [3]

    K. Yano,The theory of Lie derivatives and its application, North Holland Publ., Amsterdam, 1957.

  4. [4]

    K. Yano,Tensor fields and connections on cross-sections in the tangent bundle of a differentiable manifold, Proc. Royal Soc. of Edinburgh,67 (1967), pp. 277–288.

  5. [5]

    K. Yano -S. Kobayashi,Prolongations of tensor fields and connections to tangent bundles, I, Journ. Math. Soc. Japan,18 (1966), pp. 194–210;II, ibid.,18 (1966), pp. 236–246.

  6. [6]

    K. Yano - T. Okubo,On the tangent bundles of generalized spaces of paths, to appear in Rendic. di Mat., Roma.

  7. [7]

    K. Yano -T. Okubo,On the tangent bundles of Finsler and Riemann manifolds with Sasaki metrics, Annali di Mat. Pura ed Appl.,77 (1970), pp. 137–162.

Download references

Author information

Additional information

This work was supported by the National Research Council of Canada, 1970–1971, A-4037.

Entrata in Redazione il giorno 8 maggio 1971.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Okubo, T., Houh, C.S. Some cross-section theorems on the tangent bundle over a finslerian manifold. Annali di Matematica 92, 129 (1972) doi:10.1007/BF02417941

Download citation

Keywords

  • Vector Field
  • Tangent Bundle
  • Field Versus
  • Finslerian Manifold
  • Affine Subspace