Symplectic rigidity of geodesic flows on two-step nilmanifolds
Gordon, Carolyn S. ; Mao, Yiping ; Schueth, Dorothee
Annales scientifiques de l'École Normale Supérieure, Tome 30 (1997), p. 417-427 / Harvested from Numdam
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@article{ASENS_1997_4_30_4_417_0,
     author = {Gordon, Carolyn and Mao, Yiping and Schueth, Dorothee},
     title = {Symplectic rigidity of geodesic flows on two-step nilmanifolds},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {30},
     year = {1997},
     pages = {417-427},
     doi = {10.1016/s0012-9593(97)89927-2},
     mrnumber = {98g:53077},
     zbl = {0897.53033},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_1997_4_30_4_417_0}
}

Gordon, Carolyn S.; Mao, Yiping; Schueth, Dorothee. Symplectic rigidity of geodesic flows on two-step nilmanifolds. Annales scientifiques de l'École Normale Supérieure, Tome 30 (1997) pp. 417-427. doi : 10.1016/s0012-9593(97)89927-2. http://gdmltest.u-ga.fr/item/ASENS_1997_4_30_4_417_0/

[Cr] C. Croke, Rigidity for surfaces of non-positive curvature, (Comm. Math. Helvetici, Vol. 65, 1990, pp. 150-169). | MR 91d:53056 | Zbl 0704.53035

[CFF] C. Croke, A. Fathi and J. Feldman, The marked length spectrum of a surface of nonpositive curvature, (Topology, Vol. 31, 1992, pp. 847-858). | MR 94b:58095 | Zbl 0779.53025

[Eb] P. Eberlein, Geometry of two-step nilpotent groups with a left invariant metric, (Ann. Sci. de l'Ecole Norm. Sup., 4ème série, Vol. 27, 1994, pp. 611-660). | Numdam | MR 95m:53059 | Zbl 0820.53047

[Go] C. Gordon, The Laplace spectra versus the length spectra of Riemannian Manifolds, (Contemp. Math., Vol. 51, 1986, pp. 63-80). | MR 87i:58170 | Zbl 0591.53042

[GM1] C. Gordon and Y. Mao, Comparisons of Laplace spectra, length spectra and geodesic flow of some Riemannian manifolds, (Math. Research Letters, Vol. 1, 1994, pp. 677-688). | MR 95i:58181 | Zbl 0837.58035

[GM2] C. Gordon and Y. Mao, Geodesic conjugacy in two-step nilmanifolds, (MSRI Preprint, Vol. No. 033-95, 1995).

[GW] C. Gordon and E. Wilson, Isospectral deformations of compact solvmanifolds, (J. Diff. Geom., Vol. 19, 1984, pp. 241-256). | MR 85j:58143 | Zbl 0523.58043

[Ja] N. Jacobson, Lie Algebras, (Dover Publications, New York, 1979). | MR 80k:17001

[Ku] R. Kuwabara, A note on the deformations of Hamiltonian systems on nilmanifolds, (J. Math. Tokushima, Vol. 26, 1992, pp. 19-29). | MR 94g:58237 | Zbl 0773.58006

[Ma] F. Marhuenda, Microlocal analysis of some isospectral deformations, (Trans. Amer. Math. Soc., Vol. 343, 1994, pp. 245-275). | MR 94g:58222 | Zbl 0826.58036

[OP] H. Ouyang and H. Pesce, Déformations isospectrales sur les nilvariétés de rang deux, (C. R. Acad. Sci. Paris, sér. I., Vol. 314, 1992, pp. 621-623). | MR 93g:58152 | Zbl 0744.53029

[Ot] J. Otal, Le spectre marqué des longueurs des surfaces à courbure négative, (Ann. of Math., Vol. 131, 1990, pp. 151-162). | MR 91c:58026 | Zbl 0699.58018

[OV] A. L. Onishchik and E. B. Vinberg (eds.), Lie Groups and Lie Algebras III, (Encyclopaedia of Mathematical Sciences, Vol. 41, Springer, New York, 1991). | MR 96d:22001 | Zbl 0797.22001

[We] A. Weinstein, Fourier integral operators, quantization and the spectra of Riemannian manifolds, (Colloques Internationaux C.N.R.S., Vol. 273, 1975, pp. 289-298). | MR 58 #31307 | Zbl 0327.58013