  We derive upper eigenvalue bounds for the Dirac operator of a closed
hypersurface in a manifold with Killing spinors such as Euclidean space,
spheres or hyperbolic space. The bounds involve the Willmore functional.
Relations with the Willmore inequality are briefly discussed. In higher
codimension we obtain bounds on the eigenvalues of the Dirac operator of the
submanifold twisted with the spinor bundle of the normal bundle.
