Title: Seven dimensional cohomogeneity one manifolds with nonnegative curvature,
Abstract: We show that a certain family of cohomogeneity one manifolds does not admit
an invariant metric of nonnegative sectional curvature, unless it admits one
with positive curvature. As a consequence, the classification of nonnegatively
curved cohomogeneity one manifolds in dimension 7 is reduced to only one
further family of candidates