  A real Bott manifold is the total space of iterated RP^1 bundles starting
with a point, where each RP^1 bundle is projectivization of a Whitney sum of
two real line bundles. We prove that two real Bott manifolds are diffeomorphic
if their cohomology rings with Z/2 coefficients are isomorphic.
  A real Bott manifold is a real toric manifold and admits a flat riemannian
metric invariant under the natural action of an elementary abelian 2-group. We
also prove that the converse is true, namely a real toric manifold which admits
a flat riemannian metric invariant under the action of an elementary abelian
2-group is a real Bott manifold.
