On spherical space forms which are isospectral but not isometric

Akira IKEDA

doi:10.2969/jmsj/03530437

Akira IKEDA

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1983 Volume 35 Issue 3 Pages 437-444

DOI https://doi.org/10.2969/jmsj/03530437

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Published: 1983 Received: March 23, 1982 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) M. Berger, P. Gaudachon and E. Mazet, Le spectre d'une variété riemannienne, Lecture Notes in Math., 194, Springer-Verlag, Berlin-Heidelberg-New York, 1971.
2) A. Ikeda and Y. Yamamoto, On the spectra of 3-dimensional lens spaces, Osaka J. Math., 16 (1979), 447-469.
3) A. Ikeda, On the spectrum of a Riemannian manifold of positive constant curvature, Osaka J. Math., 17 (1980), 75-93.
4) A. Ikeda, On the spectrum of a Riemannian manifold of positive constant curvature II, Osaka J. Math., 17 (1980), 691-702.
5) A. Ikeda, On lens spaces which are isospectral but not isometric, Ann. Sci. École Norm. Sup. Sér 4 13 (1980), 303-315.
6) A. Ikeda, Isospectral problem for spherical space forms, Proc. Trance-Japan Seminar, Kyoto 1981, (to appear).
7) Y. Kitaoka, Positive definite quadratic forms with the same representation numbers, Arch. Math., 28 (1977), 495-497.
8) J. Milnor, Eigenvalues of the Laplace operator on certain manifolds, Proc. Nat. Acad. Sci. U.S.A., 51 (1964), 542.
9) M.-F. Vignéras, Variétés riemanniennes isospectrales et non isometriques, Ann. of Math., 112 (1980), 21-32.
10) G. Vincent, Les groupes lineaires finis sans points fixes, Comment. Math. Helv., 20 (1947), 117-171.
11) J. A. Wolf, Spaces of constant curvature, McGraw-Hill, 1967.

Right : [1] M. Berger, P. Gaudachon and E. Mazet, Le spectre d'une variété riemannienne, Lecture Notes in Math., 194, Springer-Verlag, Berlin-Heidelberg-New York, 1971.
[2] A. Ikeda and Y. Yamamoto, On the spectra of 3-dimensional lens spaces, Osaka J. Math., 16 (1979), 447-469.
[3] A. Ikeda, On the spectrum of a Riemannian manifold of positive constant curvature, Osaka J. Math., 17 (1980), 75-93.
[4] A. Ikeda, On the spectrum of a Riemannian manifold of positive constant curvature II, Osaka J. Math., 17 (1980), 691-702.
[5] A. Ikeda, On lens spaces which are isospectral but not isometric, Ann. Sci. École Norm. Sup. Sér 4 13 (1980), 303-315.
[6] A. Ikeda, Isospectral problem for spherical space forms, Proc. France-Japan Seminar, Kyoto 1981, (to appear).
[7] Y. Kitaoka, Positive definite quadratic forms with the same representation numbers, Arch. Math., 28 (1977), 495-497.
[8] J. Milnor, Eigenvalues of the Laplace operator on certain manifolds, Proc. Nat. Acad. Sci. U. S. A., 51 (1964), 542.
[9] M.-F. Vignéras, Variétés riemanniennes isospectrales et non isometriques, Ann. of Math., 112 (1980), 21-32.
[10] G. Vincent, Les groupes lineaires finis sans points fixes, Comment. Math. Helv., 20 (1947), 117-171.
[11] J. A. Wolf, Spaces of constant curvature, McGraw-Hill, 1967.

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