A Note on Poisson Lie Algebroids

作者: Liviu Popescu

DOI: 10.7546/GIQ-10-2009-227-236

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摘要: In this paper we generalize the linear contravariant connection on Poisson manifolds to Lie algebroids and study its tensors of torsion curvature. A which depends only bivector structural functions algebroid is given. The notions complete horizontal lifts are introduced their compatibility conditions pointed out.

参考文章(20)
Liviu Popescu, Geometrical structures on Lie algebroids Publicationes Mathematicae Debrecen. ,vol. 72, pp. 95- 110 ,(2008)
Carlo Cattani, Harmonic wavelet solution of Poisson's problem ,vol. 13, pp. 27- 37 ,(2008)
Izu Vaisman, Complementary 2-forms of Poisson structures Compositio Mathematica. ,vol. 101, pp. 55- 75 ,(1996)
Dumitru Opriş, Mihai Ivan, Gheorge Ivan, The Maxwell-Bloch equations on fractional Leibniz algebroids Balkan Journal of Geometry and its Applications (BJGA). ,vol. 13, pp. 50- 58 ,(2008)
Alan Weinstein, The local structure of Poisson manifolds Journal of Differential Geometry. ,vol. 18, pp. 523- 557 ,(1983) , 10.4310/JDG/1214437787
Eduardo Martínez, Lagrangian Mechanics on Lie Algebroids Acta Applicandae Mathematicae. ,vol. 67, pp. 295- 320 ,(2001) , 10.1023/A:1011965919259
André Lichnerowicz, Les variétés de Poisson et leurs algèbres de Lie associées Journal of Differential Geometry. ,vol. 12, pp. 253- 300 ,(1977) , 10.4310/JDG/1214433987
Gabriel Mitric, Poisson structures on cotangent bundles International Journal of Mathematics and Mathematical Sciences. ,vol. 2003, pp. 1833- 1853 ,(2003) , 10.1155/S0161171203201101