Generalized geometrical structures of odd dimensional manifolds. (English) Zbl 1163.53051

Janyška, Josef; Modugno, Marco

J. Math. Pures Appl. (9) 91, No. 2, 211-232 (2009).

This paper studies geometrical structures on the phase space of a space-time naturally induced by a metric and a phase connection. The authors first recall some standard structures; then introduce both an almost-cosymplectic-contact structure and an almost-coPoisson-Jacobi structure. These notions generalize the contact structure on a odd dimensional manifold and the Jacobi structure respectively. The general properties of these new structures are then studied. Examples are finally given. In particular, the authors present geometrical dynamical structures on the phase space of a general relativistic particle, regarded as the first jet space of motions in a spacetime.

Reviewer: Angela Gammella-Mathieu (Metz)

MSC:

53D17	Poisson manifolds; Poisson groupoids and algebroids
53D15	Almost contact and almost symplectic manifolds
53C15	General geometric structures on manifolds (almost complex, almost product structures, etc.)

Keywords:

geometrical structures; contact structures; Jacobi structure; cosymplectic-contact structure; coPoisson-Jacobi structure; phase space

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