Cotangent bundle: vector bundle T*(T*M) over T*M.
TM & TM* bundle = manifold, with twice the dimension of M
R-metric, symplectic -> TM ~ TM* (isomorphic)
trivial: TM is M * R^n form.
Cotangent bundle and HMC
cotangent bundle = phase space on which Hamiltonian mechanics plays out.
Comment is the energy for a writer, thanks!