Leo Butler - New examples of integrable geodesic flows

A geodesic flow on T^*Mⁿ is said to be integrable if it possesses n independent commuting first integrals. Taimanov has proven that if these first integrals are real analytic, then is almost abelian and H^*(M) possesses a subring isomorphic to H^*(T^d) where d is the first Betti number of M.

It will be shown that both conclusions are false in the smooth category.