Symmetric‐tensor eigenspectrum of the Laplacian on n‐spheres

M. A.

Rubin

and

C. R.

Ordóñez

, , (). All of our differential‐geometric conventions are the same as in this paper.

C. R. Ordóñez and M. A. Rubin, “Graviton Dominance in Quantum Kaluza‐Klein Theory,” University of Texas Theory Group preprint.

A.

Chodos

and

E.

Myers

, , ().

W. V. D. Hodge, Theory and Application of Harmonic Integrals (Cambridge University, Cambridge, 1952);

J. W.

 

York

,  , ();

S. M.

 

Christensen

and

M. J.

 

Duff

,   [FS1], ().

M. Christensen, M. J. Duff, G. W. Gibbons, and M. Roček, “One‐Loop Effects in Supergravity with a Cosmological Constant” (unpublished).

S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (Wiley, New York, 1972).

K. Yano, Integral Formulas in Riemannian Geometry (Dekker, New York, 1970);

M. J.

Duff

,

P. K.

Townsend

, and

P.

van Nieuwenhuizen

, , ().

L. Castellani, R. D.[Auria, P. Fré, K. Pilch, and P. van Niewenhuizen, “The Complete Mass Spectrum on $S7,$” State University of New York at Stony Brook preprint.

After obtaining our results we received a preprint (Ref. 3), which obtains by different means the same results. More recently, harmonic analysis of tensor and spinor fields on general coset spaces has been studied by the authors of Ref. 7, as well as: R. D’Auria and P. Fre, “On the Fermion Mass‐Spectrum of Kaluza‐Klein Supergravity,” State University of New York at Stony Brook preprint ITP‐SB‐83‐57;

L. Castellani, R. D’Auria, P. Fré, K. Pilch, and P. van Nieuwenhuizen, “Fermion Masses for the Englert Solution on the Round 7‐Sphere” and “The Bosonic Mass Formula for Freund‐Rubin solutions of $d = ll$ Supergravity on General Coset Manifolds,” State University of New York at Stony Brook preprints ITP‐SB‐83‐60 and ITP‐SB‐83‐61;

K. Pilch and A. N. Schellekens, “Formulae for the Eigenvalues of the Laplacian on Tensor Harmonics on Symmetric Coset Spaces,” State University of New York at Stony Brook preprint ITP‐SB‐84‐20.