On geometry of the third tangent bundle. (English) Zbl 0619.53013

The author first studies some geometrical properties of the third iterated tangent bundle T(T(TM)) of an arbitrary manifold M. Then she uses these geometrical results for an original proof of the Jacobi identity for the vector fields on M.
Reviewer: I.Kolář


53A45 Differential geometric aspects in vector and tensor analysis
58A05 Differentiable manifolds, foundations
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[1] I. Kolář: On the second tangent bundle and generalized Lie derivatives. Tensor, N. S., 38 (1982), 98-102.
[2] C. Godbillon: Géometrie différentielle et méchanique analytique. Paris (1969). · Zbl 0174.24602
[3] J. E. White: The method of iterated tangents with applications in local Riemannian geometry. Pitman 1982. · Zbl 0478.58002
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