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.
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References
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This work was supported by the National Research Council of Canada, 1970–1971, A-4037.
Entrata in Redazione il giorno 8 maggio 1971.
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Okubo, T., Houh, C.S. Some cross-section theorems on the tangent bundle over a finslerian manifold. Annali di Matematica 92, 129–138 (1972). https://doi.org/10.1007/BF02417941
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DOI: https://doi.org/10.1007/BF02417941