  Let M be a compact, connected and simply-connected Riemannian manifold, and
suppose that G is a compact, connected Lie group acting on M by isometries. The
dimension of the space of orbits is called the cohomogeneity of the action. If
the direct sum of the higher homotopy groups of M, tensored with the field of
rational numbers, is a finite-dimensional vector space over the rationals, then
M is said to be rationally elliptic. It is known that M is rationally elliptic
if it supports an action of cohomogeneity zero or one. When the cohomogeneity
is two, this general result is no longer true. However, we prove that M is
rationally elliptic in the two-dimensional case under the added assumption that
M has nonnegative sectional curvature.
