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A torus manifold   M   is a    2  n   ‐dimensional orientable manifold with an effective action of an   n  ‐dimensional torus such thatM  T   ≠  ∅   . 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   withH  odd    (  M  ;  Z  )   =  0    up to homeomorphism.

Torus manifolds and non‐negative curvature