  We prove global smooth classification results for TNS totally Anosov Z^k
actions on general compact manifolds, under each one of the following
conditions: joint integrability, resonance-free or Lyapunov pinching condition.
Unlike the previous results, we do not require any uniform quasiconformality or
pinching condition of action elements on coarse Lyapunov distributions, nor do
we have any restriction on the dimension of coarse Lyapunov distributions. The
main novelty is in proving a new standard form of the derivative cocycle for
any TNS totally Anosov Z^k action on general manifold. A main idea is to create
a new mechanism called a non-uniform redefining argument to prove continuity of
general dynamically-defined object, which should apply to more general rigidity
problems in dynamical systems.
