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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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