Generalized geometrical structures of odd dimensional manifolds
| Authors | |
|---|---|
| Year of publication | 2009 |
| Type | Article in Periodical |
| Magazine / Source | Journal de Mathematiques Pures et Appliquees |
| MU Faculty or unit | |
| 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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