Vanžurová, Alena On geometry of the third tangent bundle. (English) Zbl 0619.53013 Acta Univ. Palacki. Olomuc., Fac. Rerum Nat. 82, Math. 24, 81-96 (1985). 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 Cited in 1 Document MSC: 53A45 Differential geometric aspects in vector and tensor analysis 58A05 Differentiable manifolds, foundations Keywords:third iterated tangent bundle; Jacobi identity PDF BibTeX XML Cite \textit{A. Vanžurová}, Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 24, 81--96 (1985; Zbl 0619.53013) Full Text: EuDML OpenURL References: [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.