Torus manifolds and non-negative curvature

A torus manifold M is a 2n-dimensional orientable manifold with an effective action of an n-dimensional torus such that M-T not equal emptyset. In this paper, we discuss the classification of torus manifolds which admit an invariant metric of non-negative curvature. If M is a simply connected torus manifold which admits such a metric, then M is diffeomorphic to a quotient of a free linear torus action on a product of spheres. We also classify rationally elliptic torus manifolds M with H-odd (M; Z) = 0 up to homeomorphism.