  A harmonic map from a Riemannian manifold into a Grassmannian manifold is
characterized by a vector bundle, a space of sections of this bundle and a
Laplace operator. We apply our main theorem, itself a generalization of a
Theorem of Takahashi, to generalize the theory of do Carmo and Wallach and to
describe the moduli space of harmonic maps satisfying the gauge and the
Einstein-Hermitian conditions from a compact Rieannian manifold into a
Grassmannian. As an application, several rigidity results are exihibited. In
particular we generalize a rigidity theorem due to Calabi in the case of
holomorphic isometric immersions of compact Kaehler manifolds into complex
projective spaces. Finally, we also construct moduli spaces of holomorphic
isometric embeddings of the complex projective line into complex quadrics of
low degree.
