T-duality, Fiber Bundles and Matrices

We extend the T-duality for gauge theory to that on curved space described as a nontrivial fiber bundle. We also present a new viewpoint concerning the consistent truncation and the T-duality for gauge theory and discuss the relation between the vacua on the total space and on the base space. As examples, we consider S^3(/Z_k), S^5(/Z_k) and the Heisenberg nilmanifold.