Volume 8, issue 3 (2004)

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Tetra and Didi, the cosmic spectral twins

Peter G Doyle and Juan Pablo Rossetti

Geometry & Topology 8 (2004) 1227–1242
Bibliography
1 L Bérard-Bergery, Laplacien et géodésiques fermées sur les formes d'espace hyperbolique compactes, from: "Séminaire Bourbaki, 24ème année (1971/1972), Exp. No. 406", Springer (1973) MR0420504
2 J H Conway, J P Rossetti, Describing the platycosms arXiv:math.DG/0311476
3 J H Conway, N A Sloane, Four-dimensional lattices with the same theta series, Internat. Math. Res. Notices (1992) 93 MR1159450
4 R Gangolli, The length spectra of some compact manifolds of negative curvature, J. Differential Geom. 12 (1977) 403 MR0650997
5 C S Gordon, Isospectral manifolds with different local geometry, J. Korean Math. Soc. 38 (2001) 955 MR1849334
6 H Huber, Zur analytischen Theorie hyperbolischen Raumformen und Bewegungsgruppen, Math. Ann. 138 (1959) 1 MR0109212
7 H Huber, Zur analytischen Theorie hyperbolischer Raumformen und Bewegungsgruppen II, Math. Ann. 143 (1961) 463 MR0154980
8 R J Miatello, J P Rossetti, Flat manifolds isospectral on $p$–forms, J. Geom. Anal. 11 (2001) 649 MR1861302
9 R J Miatello, J P Rossetti, Length spectra and $p$–spectra of compact flat manifolds, J. Geom. Anal. 13 (2003) 631 MR2005157
10 J Milnor, Eigenvalues of the Laplace operator on certain manifolds, Proc. Nat. Acad. Sci. U.S.A. 51 (1964) 542 MR0162204
11 A W Reid, Isospectrality and commensurability of arithmetic hyperbolic 2- and 3–manifolds, Duke Math. J. 65 (1992) 215 MR1150584
12 J P Rossetti, J H Conway, Hearing the platycosms, Math. Res. Lett. 13 (2006) 475 MR2231133
13 A Schiemann, Ternary positive definite quadratic forms are determined by their theta series, Math. Ann. 308 (1997) 507 MR1457743
14 T Sunada, Spectrum of a compact flat manifold, Comment. Math. Helv. 53 (1978) 613 MR511851
15 J R Weeks, The shape of space, Monographs and Textbooks in Pure and Applied Mathematics 249, Marcel Dekker (2002) MR1875835
16 J R Weeks, Real-time rendering in curved spaces, IEEE Computer Graphics and Applications 22 (2002) 90