ON NONDEGENERATE EVEN-DIMENSIONAL JACOBI MANIFOLD
We give a necessary and sufficient condition to obtain a locally conformal symplectic structure from a nondegenerate Jacobi structure.
Schouten-Nijenhuis bracket, nondegenerate Jacobi structure, locally conformally symplectic manifold.
Received: May 9, 2022; Accepted: June 16, 2022; Published: August 22, 2022
How to cite this article: Norbert Mahoungou Moukala, Ange Maloko Mavambou and Vann Borhen Nkou, On nondegenerate even-dimensional Jacobi manifold, JP Journal of Geometry and Topology 28 (2022), 13-36. http://dx.doi.org/10.17654/0972415X22007
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References:
[1] N. Bourbaki, Algèbre: Chapitre 10, Algèbre homologique, Masson, Paris, New York, Barcelona, Milan, 1980.[2] L. Camille, A. P. Gengoux and P. Vanhaecke, Poisson structures, Grundlehren der mathematischen Wissenschaften 347 (2013).[3] A. Kirillov, Local Lie algebras, Russian Math. Surveys 31 (1976), 55-75.[4] J.-L. Koszul, Chochet de Schouten-Nijenhuis et Cohomologies, Astérisques, Numéro Hors Série, 1985, pp. 257-271 (in French).[5] H. C. Lee, A kind of even-dimensional differential geometry and its application to exterior calculus, Amer. J. Math. 65 (1943), 433-438.[6] A. Lichnerowicz, Les variétés de Jacobi et leurs algèbres de Lie associées, J. Math. Pures Appl. (9) 57 (1978), 453-488.[7] P. Libermann, Sur le problème d’équivalence de certaines structures infinitésimales réguliéres, Ann. Mat. Pura. Appl. (4) 36 (1954), 27-120 (in French).[8] C.-M. Marle, The Schouten-Nijenhuis bracket and interior products, J. Geom. Phys. 23(3-4) (1997), 350-359.[9] E. Okassa, Algèbres de Jacobi et algèbres de Lie-Rinehart-Jacobi, J. Pure Appl. Algebra 208(3) (2007), 1071-1089 (in French).[10] I. Vaisman, Locally conformal symplectic manifolds, Int. J. Math. Math. Sci. 8(3) (1985), 521-536.