Déformations isospectrales sur certaines nilvariétés et finitude spectrale des variétés de Heisenberg
Pesce, Hubert
Annales scientifiques de l'École Normale Supérieure, Tome 25 (1992), p. 515-538 / Harvested from Numdam
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@article{ASENS_1992_4_25_5_515_0,
     author = {Pesce, Hubert},
     title = {D\'eformations isospectrales sur certaines nilvari\'et\'es et finitude spectrale des vari\'et\'es de Heisenberg},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {25},
     year = {1992},
     pages = {515-538},
     doi = {10.24033/asens.1657},
     mrnumber = {94c:58214},
     zbl = {0777.58008},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/ASENS_1992_4_25_5_515_0}
}

Pesce, Hubert. Déformations isospectrales sur certaines nilvariétés et finitude spectrale des variétés de Heisenberg. Annales scientifiques de l'École Normale Supérieure, Tome 25 (1992) pp. 515-538. doi : 10.24033/asens.1657. http://gdmltest.u-ga.fr/item/ASENS_1992_4_25_5_515_0/

[1] M. Berger, P. Gauduchon et E. Mazet, Le spectre d'une variété riemanienne (Lecture Notes in Math., Springer, 194, 1971). | MR 43 #8025 | Zbl 0223.53034

[2] A. Borel, Introduction aux groupes arithmétiques, Hermann, Actualités scientifiques et industrielles, 1341. | MR 39 #5577 | Zbl 0186.33202

[3] D. Deturck et C. S. Gordon, Isospectral Deformations II : Trace Formulas, Metrics and Potentials (Comm. Pure Appl. Math., vol. 40, 1987, p. 367-387). | MR 88m:58186 | Zbl 0709.53030

[4] P. Eberlein, Geometry of 2-Step Nilpotent Groups with a Left Invariant Metric, Preprint de l'Université de Caroline du Nord.

[5] C. S. Gordon et E. N. Wilson, Isospectral Deformations of Compact Solvmanifolds (J. Differential Geom., vol. 19, 1984, p. 241-256). | MR 85j:58143 | Zbl 0523.58043

[6] C. S. Gordon et E. N. Wilson, Isometry Groups of Solvmanifolds (Trans. Amer. Math. Soc., vol. 307, 1988, p. 245-256). | MR 89g:53073 | Zbl 0664.53022

[7] C. S. Gordon et E. N. Wilson, The Spectrum of the Laplacian on Riemannian Heisenberg Manifolds (Michigan Math. J., vol. 33, 1986, p. 253-271). | MR 87k:58275 | Zbl 0599.53038

[8] V. Guillemin et D. Kazhdan, Some Inverse Spectral Results for Negatively Curved n-Manifolds (Proc. Symp. Pure Math., Geometry of the Laplace Operator, Amer. Math. Soc., vol. 36, 1980, p. 153-180). | MR 81i:58048 | Zbl 0456.58031

[9] V. Guillemin et D. Kazhdan, Some Inverse Spectral Results for Negatively Curved 2-Manifolds (Topology, vol. 19, 1980, p. 153-180). | Zbl 0465.58027

[10] Ikeda, Isospectral Problem for Spherical Space Forms, in Spectra of Riemannian Manifolds, M. BERGER, S. MURAKANI et T. OCHIAI éd. ; Kaigai Publication, 1983, p. 57-63.

[11] A. Kaplan, Riemannian Nilmanifolds Attached to Clifford Modules (Geom. Dedicata, vol. 11, 1981, p. 127-136). | MR 82h:22008 | Zbl 0495.53046

[12] A. Kaplan, Fundamental Solutions for a Class of Hypoelliptic PDE Generated by Composition of Quadratics Forms (Trans. Amer. Math. Soc., vol. 258, n° 1, mars 1980). | MR 81c:58059 | Zbl 0393.35015

[13] Y. Kitaoka, Positive Definite Quadratic Form with Same Representation Numbers (Arch. Math., vol. 28, 1977, p. 495-497). | MR 56 #255 | Zbl 0361.10019

[14] J. Milnor, Eigenvalues of the Laplace Operator on Certain Manifolds (Proc. Nat. Acad. Sci., vol. 51, 1964, p. 542). | MR 28 #5403 | Zbl 0124.31202

[15] J. Milnor, Curvatures of Left Invariant Metrics on Lie Groups (Advances in mathematics, vol. 21, 1976, p. 293-329). | MR 54 #12970 | Zbl 0341.53030

[16] M. Min-Oo, Spectral Rigidity for Manifolds with Negative Curvature Operator (Contemp. Math. Nonlinear Problems in Geometry, vol. 51, 1986, p. 99-103). | MR 87k:58278 | Zbl 0591.53041

[17] M. S. Raghunathan, Discrete Subgroups of Lie Groups, Springer-Verlag, New York, 1972. | MR 58 #22394a | Zbl 0254.22005

[18] T. Sunada, Riemannian Covering and Isospectral Manifolds (Ann. of Math., vol. 121, 1985, p. 169-186). | MR 86h:58141 | Zbl 0585.58047

[19] M.-F. Vigneras, Variétés riemanniennes isospectrales et non isométriques (Ann. of Math., vol. 112, 1980, p. 21-32). | MR 82b:58102 | Zbl 0445.53026

[20] S. Wolpert, The Eigenvalues Spectrum as Moduli for Flat Tori (Trans. Amer. Math. Soc., vol. 244, 1978, p. 313-321). | MR 58 #24155 | Zbl 0405.58051

[21] S. Wolpert, The Length Spectrum as Moduli for Compact Riemann Surfaces (Ann. of Math., vol. 109, 1979, p. 323-351). | MR 80j:58067 | Zbl 0441.30055