1306.5254 (Rubén Flores-Espinoza)

The Jacobi Equation and Poisson Geometry on R4    [PDF]

Rubén Flores-Espinoza

This paper is devoted to the study of solutions of the Jacobi equation in Euclidean four dimensional space R4. Each of such solutions define a Poisson tensor. Using the elementary vector calculus operations we give explicit formulas for the main geometric objets associated to the solutions of Jacobi equation, including its characteristic foliation, their symmetries and its generators, normal forms and some useful decomposition results for the solutions. In particular we study the classes of Poisson tensors of contant rank and those preserving a volume form.

View original: http://arxiv.org/abs/1306.5254