Constructing Isospectral But Non-Isometric Riemannian Manifolds
Canadian mathematical bulletin, Tome 35 (1992) no. 3, pp. 303-310

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we examine the examples of isospectral but non-isometric Riemannian manifolds given by Milnor, Ikeda, and Vignéras. Of these, only Milnor's example is accounted for by Sunada's method of constructing isospectral manifolds, and even then only as an "unnatural" construction.
DOI : 10.4153/CMB-1992-042-1
Mots-clés : 53C20, 20F34, 11R52
Chen, Sheng. Constructing Isospectral But Non-Isometric Riemannian Manifolds. Canadian mathematical bulletin, Tome 35 (1992) no. 3, pp. 303-310. doi: 10.4153/CMB-1992-042-1
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[1] 1. Boothby, W. M., An introduction to differentiable manifolds and Riemannian geometry , Academic Press, New York, 1975. Google Scholar

[2] 2. Brooks, R., Constructing isospectral manifolds, Amer. Math. Monthly, Vol. 95,8(1988), 823–839. Google Scholar

[3] 3. Buser, P., Isospectral Riemann surfaces , Ann. Inst. Fourier XXXVI( 1986), 167–192. Google Scholar

[4] 4. DeTurck, D. and Gordon, C., Isospectral deformations: Parti: Riemannian structures on two-step nilspaces, Comm. Pure. Appl. Math., 40(1987),367–387. Google Scholar

[5] 5. De Turck, D. and Gordon, C., Isospectral metric and finite Riemannian covering, Contemp. Math., 64(1987), 79–92. Google Scholar

[6] 6. Gordon, C. and Wilson, E., Isospectral deformations of compact solvmanifolds, J. Diff. Geom., 19(1984), 241–256. Google Scholar

[7] 7. Ikeda, A., On lens spaces which are isospectral but not isometric, Ann. Scient. E. Norm. Sup 13(1980), 303–315. Google Scholar

[8] 8. Milnor, J., Eigenvalues of the Laplace operators on certain manifolds , Proc. Nat. Acad. Sci. USA. 51(1964), 542. Google Scholar

[9] 9. O'Meara, O. T., Introduction to quadratic forms , Springer, New York, (1973). Google Scholar

[10] 10. Perlis, R., On the equation ζ(s) = ζ′(s), J. NumberTh. (3) 9(1977), 342–360. Google Scholar

[11] 11. Serre, J. -P., A course in arithmetic , Springer, New York, (1973). Google Scholar

[12] 12. Sunada, T., Riemannian coverings and isospectral manifolds, Ann. Math. 121(1985), 169–186. Google Scholar

[13] 13. Vignéras, M. F., Arithmétique des algèbres de quaternions , Springer-Verlag Lecture Notes 800(1980). Google Scholar

[14] 14. Vignéras, M. F., Variétés riemaniennes isospectrales et non isométriques, Ann. of Math. 112(1980), 21–32. Google Scholar

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