Déformations isospectrales sur certaines nilvariétés et finitude spectrale des variétés de Heisenberg
Annales scientifiques de l'École Normale Supérieure (1992)
- Volume: 25, Issue: 5, page 515-538
- ISSN: 0012-9593
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topPesce, Hubert. "Déformations isospectrales sur certaines nilvariétés et finitude spectrale des variétés de Heisenberg." Annales scientifiques de l'École Normale Supérieure 25.5 (1992): 515-538. <http://eudml.org/doc/82326>.
@article{Pesce1992,
author = {Pesce, Hubert},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {nilpotent Lie group; isospectral deformations; almost linear automorphisms},
language = {fre},
number = {5},
pages = {515-538},
publisher = {Elsevier},
title = {Déformations isospectrales sur certaines nilvariétés et finitude spectrale des variétés de Heisenberg},
url = {http://eudml.org/doc/82326},
volume = {25},
year = {1992},
}
TY - JOUR
AU - Pesce, Hubert
TI - Déformations isospectrales sur certaines nilvariétés et finitude spectrale des variétés de Heisenberg
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1992
PB - Elsevier
VL - 25
IS - 5
SP - 515
EP - 538
LA - fre
KW - nilpotent Lie group; isospectral deformations; almost linear automorphisms
UR - http://eudml.org/doc/82326
ER -
References
top- [1] M. BERGER, P. GAUDUCHON et E. MAZET, Le spectre d'une variété riemanienne (Lecture Notes in Math., Springer, 194, 1971). Zbl0223.53034MR43 #8025
- [2] A. BOREL, Introduction aux groupes arithmétiques, Hermann, Actualités scientifiques et industrielles, 1341. Zbl0186.33202MR39 #5577
- [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). Zbl0709.53030MR88m:58186
- [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). Zbl0523.58043MR85j:58143
- [6] C. S. GORDON et E. N. WILSON, Isometry Groups of Solvmanifolds (Trans. Amer. Math. Soc., vol. 307, 1988, p. 245-256). Zbl0664.53022MR89g:53073
- [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). Zbl0599.53038MR87k:58275
- [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). Zbl0456.58031MR81i:58048
- [9] V. GUILLEMIN et D. KAZHDAN, Some Inverse Spectral Results for Negatively Curved 2-Manifolds (Topology, vol. 19, 1980, p. 153-180). Zbl0465.58027
- [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). Zbl0495.53046MR82h:22008
- [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). Zbl0393.35015MR81c:58059
- [13] Y. KITAOKA, Positive Definite Quadratic Form with Same Representation Numbers (Arch. Math., vol. 28, 1977, p. 495-497). Zbl0361.10019MR56 #255
- [14] J. MILNOR, Eigenvalues of the Laplace Operator on Certain Manifolds (Proc. Nat. Acad. Sci., vol. 51, 1964, p. 542). Zbl0124.31202MR28 #5403
- [15] J. MILNOR, Curvatures of Left Invariant Metrics on Lie Groups (Advances in mathematics, vol. 21, 1976, p. 293-329). Zbl0341.53030MR54 #12970
- [16] M. MIN-OO, Spectral Rigidity for Manifolds with Negative Curvature Operator (Contemp. Math. Nonlinear Problems in Geometry, vol. 51, 1986, p. 99-103). Zbl0591.53041MR87k:58278
- [17] M. S. RAGHUNATHAN, Discrete Subgroups of Lie Groups, Springer-Verlag, New York, 1972. Zbl0254.22005MR58 #22394a
- [18] T. SUNADA, Riemannian Covering and Isospectral Manifolds (Ann. of Math., vol. 121, 1985, p. 169-186). Zbl0585.58047MR86h:58141
- [19] M.-F. VIGNERAS, Variétés riemanniennes isospectrales et non isométriques (Ann. of Math., vol. 112, 1980, p. 21-32). Zbl0445.53026MR82b:58102
- [20] S. WOLPERT, The Eigenvalues Spectrum as Moduli for Flat Tori (Trans. Amer. Math. Soc., vol. 244, 1978, p. 313-321). Zbl0405.58051MR58 #24155
- [21] S. WOLPERT, The Length Spectrum as Moduli for Compact Riemann Surfaces (Ann. of Math., vol. 109, 1979, p. 323-351). Zbl0441.30055MR80j:58067
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