Let (Mi, αi), i = 1, 2, be two smooth manifolds equipped with symplectic, contact or volume forms αi. We show that if a group isomorphism between the automorphism groups of αi is induced by a bijective map between MMi, then this map must be a C∞ diffeomorphism which exchanges the structures αi. This generalizes a theorem of Takens.
All Science Journal Classification (ASJC) codes
- Applied Mathematics