Generalized geometrical structures of odd dimensional manifolds

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Authors

JANYŠKA Josef MODUGNO Marco

Year of publication 2009
Type Article in Periodical
Magazine / Source Journal de Mathematiques Pures et Appliquees
MU Faculty or unit

Faculty of Science

Citation
Web http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VMD-4TK92JF-5&_user=606226&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000031418&_version=1&_urlVersion=0&_userid=606226&md5=d6a2e11bb27ecdaeecd5e32d01570103
Field General mathematics
Keywords Spacetime; Phase space; Phase connection; Schouten bracket; Frölicher Nijenhuis bracket; Cosymplectic structure; coPoisson structure; Contact structure; Jacobi structure; Almost cosymplectic contact structure; Almost coPoisson Jacobi structure
Description We define an almost cosymplectic contact structure which generalizes cosymplectic and contact structures of an odd dimensional manifold. Analogously, we define an almost coPoisson Jacobi structure which generalizes a Jacobi structure. Moreover, we study relations between these structures and analyse the associated algebras of functions. As examples of the above structures, we present geometrical dynamical structures of the phase space of a general relativistic particle, regarded as the 1st jet space of motions in a spacetime. We describe geometric conditions by which a metric and a connection of the phase space yield cosymplectic and dual coPoisson structures, in case of a spacetime with absolute time (a Galilei spacetime), or almost cosymplectic contact and dual almost coPoisson Jacobi structures, in case of a spacetime without absolute time (an Einstein spacetime).
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