On exact Poisson structures

被引：0
|
作者：
Yi, Yingfei [1 ]
Zhang, Xiang [2 ]
机构：
[1] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA
[2] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China
来源：
NONLINEAR DYNAMICS AND EVOLUTION EQUATIONS | 2006年 / 48卷
关键词：
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
By studying the exactness of multi-linear vectors on an orientable smooth manifold M, we give some characterizations to exact Poisson structures defined on M and study general properties of these structures. Following recent works [12, 13, 15], we will pay particular attention to the classification of some special classes of exact Poisson structures such as Jacobian and quasi-homogeneous Poisson structures. A characterization of exact Poisson structures which are invariant under the flow of a class of completely integrable systems will also be given.
引用
收藏
页码：291 / +
页数：3
相关论文
共 50 条
  • [21] Formal Poisson Cohomology of Quadratic Poisson Structures
    Philippe Monnier
    Letters in Mathematical Physics, 2002, 59 : 253 - 267
  • [22] On linearized Poisson structures
    Vorobjev, YM
    MATHEMATICAL NOTES, 2001, 70 (3-4) : 486 - 493
  • [23] ON QUADRATIC POISSON STRUCTURES
    LIU, ZJ
    XU, P
    LETTERS IN MATHEMATICAL PHYSICS, 1992, 26 (01) : 33 - 42
  • [24] Homogeneous Poisson structures
    Malek, F
    Abad, ASD
    BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1996, 54 (02) : 203 - 210
  • [25] Averaging of Poisson Structures
    Vorobiev, Yuri
    GEOMETRIC METHODS IN PHYSICS, 2008, 1079 : 235 - 240
  • [26] On Linearized Poisson Structures
    Yu. M. Vorobjev
    Mathematical Notes, 2001, 70 : 486 - 493
  • [27] Transposed Poisson Structures
    Patrícia Damas Beites
    Bruno Leonardo Macedo Ferreira
    Ivan Kaygorodov
    Results in Mathematics, 2024, 79
  • [28] Classification of Poisson structures
    Lychagina, OV
    DOKLADY AKADEMII NAUK, 1996, 350 (03) : 304 - 307
  • [29] Generalized Poisson structures
    de Azcarraga, JA
    Perelomov, AM
    Bueno, JCP
    GROUP 21 - PHYSICAL APPLICATIONS AND MATHEMATICAL ASPECTS OF GEOMETRY, GROUPS, AND ALGEBRA, VOLS 1 AND 2, 1997, : 884 - 888
  • [30] Quivers and Poisson structures
    Bielawski, Roger
    MANUSCRIPTA MATHEMATICA, 2013, 141 (1-2) : 29 - 49
12345