Geometric structures on the tangent bundle of the Einstein spacetime

We describe conditions under which a spacetime connection and a scaled Lorentzian metric define natural symplectic and Poisson structures on the tangent bundle of the Einstein spacetime

On the characterization of infinitesimal symmetries of the relativistic phase space

The phase space of relativistic particle mechanics is defined as the 1st jet space of motions regarded as timelike 1-dimensional submanifolds of spacetime. A Lorentzian metric and an electromagnetic 2-form define naturally on the odd-dimensional phase space a generalized contact structure. In the paper infinitesimal symmetries of the phase structures are characterized. More precisely, it is proved that all phase infinitesimal symmetries are special Hamiltonian lifts of distinguished conserved quantities on the phase space. It is proved that generators of infinitesimal symmetries constitute a Lie algebra with respect to a special bracket. A momentum map for groups of symmetries of the geometric structures is provided.Comment: 38 page

Relations between constants of motion and conserved functions

We study relations between functions on the cotangent bundle of a spacetime which are constants of motion for geodesics and functions on the odd--dimensional phase space conserved by the Reeb vector fields of geometrical structures generated by the metric and an electromagnetic field.Jsou studovány vztahy mezi funkcemi na kotečném byndlu prostoročasu, které jsou konstantní na geodetických křivkách a funkcemi na licho-dimenzionálním fázovém prostoru konzervované vzhledem k Reebovu vektorovému poli geometrických struktur daných metrickým a elektromagnetickým polem.We study relations between functions on the cotangent bundle of a spacetime which are constants of motion for geodesics and functions on the odd--dimensional phase space conserved by the Reeb vector fields of geometrical structures generated by the metric and an electromagnetic field

On Lie algebras of generators of infinitesimal symmetries of almost-cosymplectic-contact structures

We study Lie algebras of generators of infinitesimal symmetries of almost-cosymplectic-contact structures of odd dimensional manifolds. The almost-cosymplectic-contact structure admits on the sheaf of pairs of 1-forms and functions the structure of a Lie algebra. We describe Lie subalgebras in this Lie algebra given by pairs generating infinitesimal symmetries of basic tensor fields given by the almost-cosymplectic-contact structure.Jsou studovány Lie algebry generátorů infinitesimálních symetrií skoro-kosymplectických-kontaktních structur licho-dimenzionálnách variet. Skoro-kosymplectická-kontaktní structura určuje na množině dvojic tvořených 1-formami a funkcemi strukturu Lieovy algebry. Jsou popsány Lieovy podalgebry v této Lieově algebře určené dvojicemi, které generují infinitesimální symetrie základních tenzorových polí daných skoro-kosymplectickou-kontaktní structurou.We study Lie algebras of generators of infinitesimal symmetries of almost-cosymplectic-contact structures of odd dimensional manifolds. The almost-cosymplectic-contact structure admits on the sheaf of pairs of 1-forms and functions the structure of a Lie algebra. We describe Lie subalgebras in this Lie algebra given by pairs generating infinitesimal symmetries of basic tensor fields given by the almost-cosymplectic-contact structure