@article{ASENS_1994_4_27_5_611_0, author = {Eberlein, Patrick}, title = {Geometry of $2$-step nilpotent groups with a left invariant metric}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, volume = {27}, year = {1994}, pages = {611-660}, doi = {10.24033/asens.1702}, mrnumber = {95m:53059}, zbl = {0820.53047}, language = {en}, url = {http://dml.mathdoc.fr/item/ASENS_1994_4_27_5_611_0} }
Eberlein, Patrick. Geometry of $2$-step nilpotent groups with a left invariant metric. Annales scientifiques de l'École Normale Supérieure, Tome 27 (1994) pp. 611-660. doi : 10.24033/asens.1702. http://gdmltest.u-ga.fr/item/ASENS_1994_4_27_5_611_0/
[A] Mathematical Methods of classical Mechanics (Graduate Texts in Mathematics, Vol. 60, Springer-Verlag, 1980). | Zbl 0386.70001
,[Ba]
, personal communication.[BG] Isospectral Famillies of Conformally Equivalent Riemannian Metrics (Bull. Amer. Math. Soc., Vol. 23, 1990, pp. 433-436). | MR 91a:58188 | Zbl 0722.58045
and ,[BGM] Le spectre d'une variété Riemannienne (Springer Lecture Notes, Vol. 194, New York, 1971). | MR 43 #8025 | Zbl 0223.53034
, and ,[CDKR] H-type Groups and Iwasawa Decompositions (Advances in Math., Vol. 87, 1991, pp. 1-41). | MR 92e:22017 | Zbl 0761.22010
, , and ,[CE] Comparison Theorems in Riemannian geometry, North-Holland, Amsterdam, 1975. | MR 56 #16538 | Zbl 0309.53035
and ,[D1] Audible and Inaudible Geometric Properties (Proc. of Conference on Differential Geometry and Topology, Rendiconti Sem. della Facolta Sci. dell' Univ. di Cagliari, 58, 1988-Supplement, pp. 1-26). | MR 92i:58197
,[D2] The Geometry of Isospectral Deformations (to appear in Proc. Sympos. Pure Math., Summer Geomety Institute, July 1990).
,[DG1] Isospectral Deformations I : Riemannian Structures on 2-step Nilspaces (Comm. Pure and Applied Math., Vol. 40, 1987, pp. 367-387). | MR 88m:58186 | Zbl 0649.53025
and ,[DG2] Isospectral Deformations II : Trace Formulas, Metrics and Potentials (Comm. Pure and Applied Math., Vol. 42, 1989, pp. 1067-1095). | MR 91e:58197 | Zbl 0709.53030
and ,[DG3] Isospectral Metrics and Finite Riemannian Coverings (Contemp. Math., Vol. 64, 1987, pp. 79-92). | MR 88d:58124 | Zbl 0646.58030
and ,[DGGW1] You Cannot Hear the Mass of a Homology Class (Comment. Math. Helvetici, Vol. 64, 1989, pp. 589-617). | MR 90k:58233 | Zbl 0694.53037
, , and ,[DGGW2] How Can a Drum Change Shape While Sounding the Same ?, in Differential Geometry : Symposium in Honor of Manfredo do Carmo, ed. B. Lawson and K. Tenenblatt (Pitman Surveys in Pure and Applied Math., Vol. 52, 1991, pp. 111-122). | MR 93f:58236 | Zbl 0728.58039
, , and ,[DGGW3] How Can a Drum Change Shape While Sounding the Same ?, Part 2, in Mechanics, Analysis and Geometry, 200 Years After Lagrange, ed. M. Francaviglia, Elsevier Press, 1991, pp. 335-358. | MR 93f:58237 | Zbl 0728.58040
, , and ,[DGGW4] The Inaudible Geometry of Nilmanifolds (Invent. Math., Vol. 111, 1993, pp. 271-284). | MR 93k:58222 | Zbl 0779.53026
, , and ,[DGGW5] Conformal Isospectral Deformations (Indiana Univ. Math. Jour., Vol. 41, 1992, pp. 99-107). | MR 93c:58218 | Zbl 0742.58055
, , and ,[E1] Geometry of 2-step Nilpotent Groups with a Left Invariant Metric, II (Trans. Amer. Math. Soc., Vol. 343, 1994, pp. 805-828). | MR 95b:53061 | Zbl 0830.53039
,[E2] Geometry of Nonpositively Curved Manifolds lecture notes, to appear, in Univ. Chicago Press.
,[G1] The Laplace Spectra Versus the Length Spectral of Riemannian Manifolds (Contemp. Math., Vol. 51, 1986, pp. 63-80). | MR 87i:58170 | Zbl 0591.53042
,[G2] Riemannian Manifolds Isospectral on Functions but not on 1-forms (J. Diff. Geom., Vol. 24, 1986, pp. 79-96). | MR 87m:58174 | Zbl 0585.53036
,[G3]
, personal communication.[GW1] Isospectral Deformations of Compact Solvmanifolds (J. Diff. Geom., Vol. 19, 1984, pp. 241-256). | MR 85j:58143 | Zbl 0523.58043
and ,[GW2] The Spectrum of the Laplacian on Riemannian Heisenberg manifolds (Michigan Math. Jour., Vol. 33, 1986, pp. 253-271). | MR 87k:58275 | Zbl 0599.53038
and ,[Hei] On Homogeneous Manifolds of Negative Curvature, (Math. Annalen, Vol. 211, 1974, pp. 23-34). | MR 50 #5695 | Zbl 0273.53042
,[Hel] Differential Geometry and Symmetric Spaces, Academic Press, New York, 1962. | MR 26 #2986 | Zbl 0111.18101
,[K1] Riemannian Nilmanifolds Attached to Clifford Modules, (Geom. Dedicata, Vol. 11, 1981, pp. 127-136). | MR 82h:22008 | Zbl 0495.53046
,[K2] On the Geometry of the Groups of Heisenberg Type (Bull. London Math. Soc., Vol. 15, 1983, pp. 35-42). | MR 84h:53063 | Zbl 0521.53048
,[Ka] The Geometry of Geodesics and the Eigenfunctions of the Beltrami-Laplace Operator on Symmetric Spaces (Trans. Moscow Math. Soc., Tome 14, 1965, AMS Translation, pp. 51-199). | MR 37 #6876 | Zbl 0164.22202
,[Ko] Geometric Properties of Heisenberg Type Groups, (Advances in Math., Vol. 56, 1985, pp. 28-38). | MR 86h:53050 | Zbl 0589.53053
,[Ma] Closed Geodesics in 2-step Nilmanifolds, dissertation, Univ. of N. Carolina, 1992.
,[Mi] Curvatures of Left Invariant Metrics on Lie Groups, (Advances in Math., Vol. 21, 1976, pp. 293-329). | MR 54 #12970 | Zbl 0341.53030
,[PS] Torus Bundles Over a Torus (Proc. Amer. Math. Soc., Vol. 12, 1961, pp. 26-29). | MR 23 #A963 | Zbl 0102.38702
and ,[R] Discrete Subgroups of Lie Groups, Springer, New York, 1972. | MR 58 #22394a | Zbl 0254.22005
,[St] Topology of Fibre Bundles, Princeton Univ. Press, Princeton, 1951. | MR 12,522b | Zbl 0054.07103
,[Wi] Isometry Groups on Homogeneous Nilmanifolds (Geom. Dedicata, Vol. 12, 1982, pp. 337-346). | MR 84a:53048 | Zbl 0489.53045
,[Wo1] Curvature in Nilpotent Lie Groups (Proc. Amer. Math. Soc., Vol. 15, 1964, pp. 271-274). | MR 28 #5405 | Zbl 0134.17905
,[Wo2] On locally Symmetric Spaces of Nonnegative Curvature and Certain Other Locally Symmetric Spaces (Comm. Math. Helv., Vol. 37, 1963, p. 265-295, plus typewritten erratum). | Zbl 0113.37101
,