A. IKEDA AND Y. TANIGUCHI eigenfunctions have been obtained by the restriction to S n and P n (C) of the harmonic homogeneous polynomials on R n+1 and C n+1 (cf. [12] ). In 6 (Theorem 6.8) and 7 (Theorem 7.13), we give the analogy for differential forms on S n and P n (C) using harmonic polynomial forms. The authors express their hearty gratitude to Prof. H. Ozeki for valuable suggestions and discussions. SPECTRA AND EIGENFORMS OF THE LAPLACIAN 517 Έt = {φ<=Ei; dφ = 0}, "E{ = iφeEt; Sφ = 0} , which are both G-submodules of E{. We see