JP Journal of Geometry and Topology

The JP Journal of Geometry and Topology publishes articles in all branches of geometry and topology, with applications to physics. It covers areas such as differential geometry, algebraic topology, and geometric aspects of mathematical physics. Survey articles are also welcome.

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ON NONDEGENERATE EVEN-DIMENSIONAL JACOBI MANIFOLD

Authors

  • Norbert Mahoungou Moukala
  • Ange Maloko Mavambou
  • Vann Borhen Nkou

Keywords:

Schouten-Nijenhuis bracket, nondegenerate Jacobi structure, locally conformally symplectic manifold.

DOI:

https://doi.org/10.17654/0972415X22007

Abstract

We give a necessary and sufficient condition to obtain a locally conformal symplectic structure from a nondegenerate Jacobi structure.

Received: May 9, 2022  
Accepted: June 16, 2022 

References

N. Bourbaki, Algèbre: Chapitre 10, Algèbre homologique, Masson, Paris, New York, Barcelona, Milan, 1980.

L. Camille, A. P. Gengoux and P. Vanhaecke, Poisson structures, Grundlehren der mathematischen Wissenschaften 347 (2013).

A. Kirillov, Local Lie algebras, Russian Math. Surveys 31 (1976), 55-75.

J.-L. Koszul, Chochet de Schouten-Nijenhuis et Cohomologies, Astérisques, Numéro Hors Série, 1985, pp. 257-271 (in French).

H. C. Lee, A kind of even-dimensional differential geometry and its application to exterior calculus, Amer. J. Math. 65 (1943), 433-438.

A. Lichnerowicz, Les variétés de Jacobi et leurs algèbres de Lie associées, J. Math. Pures Appl. (9) 57 (1978), 453-488.

P. Libermann, Sur le problème d’équivalence de certaines structures infinitésimales réguliéres, Ann. Mat. Pura. Appl. (4) 36 (1954), 27-120 (in French).

C.-M. Marle, The Schouten-Nijenhuis bracket and interior products, J. Geom. Phys. 23(3-4) (1997), 350-359.

E. Okassa, Algèbres de Jacobi et algèbres de Lie-Rinehart-Jacobi, J. Pure Appl. Algebra 208(3) (2007), 1071-1089 (in French).

I. Vaisman, Locally conformal symplectic manifolds, Int. J. Math. Math. Sci. 8(3) (1985), 521-536.

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Published

2022-08-22

Issue

Vol. 28 (2022)

Section

Articles

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How to Cite

ON NONDEGENERATE EVEN-DIMENSIONAL JACOBI MANIFOLD. (2022). JP Journal of Geometry and Topology, 28, 13-36. https://doi.org/10.17654/0972415X22007

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