关键词: Jacobi结构, Poisson结构, 1-闭链, 分类

Abstract:

Using the method in Poisson geometry, the author proved that a linear Jacobi structure corresponds to a linear Poisson structure and a 1-cocycle. Thus, by the classification of linear Poisson structures on R³,  the classification of linear Jacobi structures on R³ is obtained after computing the first cohomology.

Key words: Jacobi structures, Poisson structures, 1-cocycles, classification