Journal of Differential Geometry

Isospectral deformations of compact solvmanifolds

Carolyn S. Gordon and Edward N. Wilson

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Article information

J. Differential Geom., Volume 19, Number 1 (1984), 241-256.

First available in Project Euclid: 26 June 2008

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 58G25
Secondary: 22E25: Nilpotent and solvable Lie groups 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]


Gordon, Carolyn S.; Wilson, Edward N. Isospectral deformations of compact solvmanifolds. J. Differential Geom. 19 (1984), no. 1, 241--256. doi:10.4310/jdg/1214438431.

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  • [1] M. Berger, P. Gauduchon and E. Mazet, Le spectre d'une variete Riemannienne, Lecture Notes in Math., Vol. 194, Springer, Berlin and New York, 1971.
  • [2] C. S. Gordon and E. N. Wilson, Isometry groups of solvmanifolds, submitted for publication.
  • [3] V. Guillemin and D. Kazhdan, Some inverse spectral results for negatively curved two manifolds, Topology 19 (1980) 301-312.
  • [4] S. Helgason, Differential geometry, Lie groups, and symmetric spaces, Academic Press, New York, 1978.
  • [5] A. Ikeda, On the spectrum of a Riemannian manifold of positive constant curvature, Osaka J. Math. 17 (1980) 75-93; 691-702.
  • [6] C. C. Moore, Representations of solvable and nilpotent groups and harmonic analysis on nil and solvmanifolds, Proc. Sympos. Pure Math., Vol. 26, Amer. Math. Soc, Providence, RI, 1973, 3-44.
  • [7] L. Pukanszky, Lecons sur les representations des groupes, Dunod, Paris, 1966.
  • [8] M. S. Raghunathan, Discrete subgroups of Lie groups, Springer, Berlin and New York, 1972.
  • [9] G. de Rham, Varietes differentiates, Hermann, Paris, 1960.
  • [10] U. Simon and H. Wissner, Geometry of the Laplace operator, preprint, Technische Universitat Berlin.
  • [11] H. Urakawa, Bounded domains which are isospectral but not isometric, Ann. Sci. Ecole Norm. Sup. (4) 15( 1982) 441-456.
  • [12] M.-F. Vigneras, Varietes riemanniennes isospectrales et non isometriques, Ann. of Math. 112 (1980) 21-32.