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Sur quelques propriétés de géométrie homogène. (On certain properties of homogeneous geometry). (French) Zbl 0616.53025

Géométrie symplectique et mécanique, Rencontre Balaruc/France 1983, Sémin. sud-rhodanien Géom., 91-106 (1985).
[For the entire collection see Zbl 0606.00019.]
This paper is a synthesis of the theory of jets, the contact elements of superior order and the foliations of second order on the one hand and some ideas of Finsler spaces on the other hand. The author presents the fiber bundles associated to a surjective submersion, the semi-basic and vertical differential forms, the holonomic vector fields, the sprays, presprays and foliations of second order, endomorphisms and isomorphisms associated to a prespray, connections associated to sprays and presprays and Legendre homogeneous transformations.
Reviewer: C.L.Bejan

MSC:

53C12 Foliations (differential geometric aspects)
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
58A20 Jets in global analysis

Citations:

Zbl 0606.00019