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@article{819792, author = {Janyška, Josef and Modugno, Marco}, article_location = {Francie}, article_number = {2}, 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}, language = {eng}, issn = {0021-7824}, journal = {Journal de Mathematiques Pures et Appliquees}, title = {Generalized geometrical structures of odd dimensional manifolds}, url = {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}, volume = {91}, year = {2009} }
TY - JOUR ID - 819792 AU - Janyška, Josef - Modugno, Marco PY - 2009 TI - Generalized geometrical structures of odd dimensional manifolds JF - Journal de Mathematiques Pures et Appliquees VL - 91 IS - 2 SP - 211-232 EP - 211-232 PB - Elsevier SAS SN - 00217824 KW - Spacetime KW - Phase space KW - Phase connection KW - Schouten bracket KW - Frölicher Nijenhuis bracket KW - Cosymplectic structure KW - coPoisson structure KW - Contact structure KW - Jacobi structure KW - Almost cosymplectic contact structure KW - Almost coPoisson Jacobi structure UR - 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 N2 - 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). ER -
JANYŠKA, Josef and Marco MODUGNO. Generalized geometrical structures of odd dimensional manifolds. \textit{Journal de Mathematiques Pures et Appliquees}. Francie: Elsevier SAS, 2009, vol.~91, No~2, p.~211-232. ISSN~0021-7824.
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