Annali di Matematica Pura ed Applicata. December , Cite as. On the basis of the so-called phase completion the notion of vertical, horizontal and complete objects is defined in the tangent bundles over Finslerian and Riemannian manifold. Such a tangent bundle is made into a manifold of almost Kaehlerian structure by endowing it with Sasakian metric. The components of curvature tensors with respect to the adapted frame are presented. This having been done it is shown possible to study the differential geometry of Finslerian spaces by dealing with that of their own tangent bundles.

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Caratheodory , Variationsrechnung und partielle Differentialgleichungen erster Ordnung , Berlin und Leibzig Google Scholar. Cartan , Les espaces de Finsler , Act. Davies , Areal spaces , Annali di Mat, 55 63— Math 4 45— CrossRef Google Scholar. Douglas , The general geometry of paths. Doyle , Tensor decomposition with applications to the contact and complex groups , Ann. Eisenhart , Finsler space derived from Riemann space by contact transformations , Ann. Eisenhart and M. Knebelman , Invariant theory of homogeneous contact transformations , Ann.

Knebelman , Collineations and motions in the generalized spaces of paths , Amer. Kobayashi and K. Nomiza , Foundation of differential geometry , 1, Interscience Tract. Dennis Sullivan Publications. Thesis, Princeton. See []. Preprint, Univ. Preprint Univ. Topology 9 , MIT , Mimeogr.

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Notes in Math. Deligne, P. Griffiths, J. See also Seminaire Bourbaki, Vol. Lecture notes in Math. AMS 81, , Paris A. Pari Ser. A-B, , AA Journal of Diff. Geometry 11 , Topology 15 , IHES 46 , Orsay , Asterisque no. Edwards, K.

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