A survey of Nambu–Poisson geometry

We survey geometry of Nambu–Poisson manifolds. First we recall Nambu's work which is the origin of Nambu–Poisson geometry. Next adopting Takhtajan's geometric formulation and applying the local structure theorem of Nambu–Poisson tensors, we study the projectability of left invariant Nambu–Poisson tensors on Lie groups to certain homogeneous spaces.