  A Riemannian manifold is called geometrically formal if the wedge product of
harmonic forms is again harmonic, which implies in the compact case that the
manifold is topologically formal in the sense of rational homotopy theory. A
manifold admitting a Riemannian metric of positive sectional curvature is
conjectured to be topologically formal. Nonetheless, we show that among the
homogeneous Riemannian metrics of positive sectional curvature a geometrically
formal metric is either symmetric, or a metric on a rational homology sphere.
