@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}, pages = {611--660}, publisher = {Elsevier}, volume = {Ser. 4, 27}, number = {5}, year = {1994}, doi = {10.24033/asens.1702}, mrnumber = {95m:53059}, zbl = {0820.53047}, language = {en}, url = {http://archive.numdam.org/articles/10.24033/asens.1702/} }
TY - JOUR AU - Eberlein, Patrick TI - Geometry of $2$-step nilpotent groups with a left invariant metric JO - Annales scientifiques de l'École Normale Supérieure PY - 1994 SP - 611 EP - 660 VL - 27 IS - 5 PB - Elsevier UR - http://archive.numdam.org/articles/10.24033/asens.1702/ DO - 10.24033/asens.1702 LA - en ID - ASENS_1994_4_27_5_611_0 ER -
%0 Journal Article %A Eberlein, Patrick %T Geometry of $2$-step nilpotent groups with a left invariant metric %J Annales scientifiques de l'École Normale Supérieure %D 1994 %P 611-660 %V 27 %N 5 %I Elsevier %U http://archive.numdam.org/articles/10.24033/asens.1702/ %R 10.24033/asens.1702 %G en %F 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, Série 4, Tome 27 (1994) no. 5, pp. 611-660. doi : 10.24033/asens.1702. http://archive.numdam.org/articles/10.24033/asens.1702/
[A] Mathematical Methods of classical Mechanics (Graduate Texts in Mathematics, Vol. 60, Springer-Verlag, 1980). | Zbl
,[Ba]
, personal communication.[BG] Isospectral Famillies of Conformally Equivalent Riemannian Metrics (Bull. Amer. Math. Soc., Vol. 23, 1990, pp. 433-436). | MR | Zbl
and ,[BGM] Le spectre d'une variété Riemannienne (Springer Lecture Notes, Vol. 194, New York, 1971). | MR | Zbl
, and ,[CDKR] H-type Groups and Iwasawa Decompositions (Advances in Math., Vol. 87, 1991, pp. 1-41). | MR | Zbl
, , and ,[CE] Comparison Theorems in Riemannian geometry, North-Holland, Amsterdam, 1975. | MR | Zbl
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
,[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 | Zbl
and ,[DG2] Isospectral Deformations II : Trace Formulas, Metrics and Potentials (Comm. Pure and Applied Math., Vol. 42, 1989, pp. 1067-1095). | MR | Zbl
and ,[DG3] Isospectral Metrics and Finite Riemannian Coverings (Contemp. Math., Vol. 64, 1987, pp. 79-92). | MR | Zbl
and ,[DGGW1] You Cannot Hear the Mass of a Homology Class (Comment. Math. Helvetici, Vol. 64, 1989, pp. 589-617). | MR | Zbl
, , 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 | Zbl
, , 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 | Zbl
, , and ,[DGGW4] The Inaudible Geometry of Nilmanifolds (Invent. Math., Vol. 111, 1993, pp. 271-284). | MR | Zbl
, , and ,[DGGW5] Conformal Isospectral Deformations (Indiana Univ. Math. Jour., Vol. 41, 1992, pp. 99-107). | MR | Zbl
, , 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 | Zbl
,[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 | Zbl
,[G2] Riemannian Manifolds Isospectral on Functions but not on 1-forms (J. Diff. Geom., Vol. 24, 1986, pp. 79-96). | MR | Zbl
,[G3]
, personal communication.[GW1] Isospectral Deformations of Compact Solvmanifolds (J. Diff. Geom., Vol. 19, 1984, pp. 241-256). | MR | Zbl
and ,[GW2] The Spectrum of the Laplacian on Riemannian Heisenberg manifolds (Michigan Math. Jour., Vol. 33, 1986, pp. 253-271). | MR | Zbl
and ,[Hei] On Homogeneous Manifolds of Negative Curvature, (Math. Annalen, Vol. 211, 1974, pp. 23-34). | MR | Zbl
,[Hel] Differential Geometry and Symmetric Spaces, Academic Press, New York, 1962. | MR | Zbl
,[K1] Riemannian Nilmanifolds Attached to Clifford Modules, (Geom. Dedicata, Vol. 11, 1981, pp. 127-136). | MR | Zbl
,[K2] On the Geometry of the Groups of Heisenberg Type (Bull. London Math. Soc., Vol. 15, 1983, pp. 35-42). | MR | Zbl
,[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 | Zbl
,[Ko] Geometric Properties of Heisenberg Type Groups, (Advances in Math., Vol. 56, 1985, pp. 28-38). | MR | Zbl
,[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 | Zbl
,[PS] Torus Bundles Over a Torus (Proc. Amer. Math. Soc., Vol. 12, 1961, pp. 26-29). | MR | Zbl
and ,[R] Discrete Subgroups of Lie Groups, Springer, New York, 1972. | MR | Zbl
,[St] Topology of Fibre Bundles, Princeton Univ. Press, Princeton, 1951. | MR | Zbl
,[Wi] Isometry Groups on Homogeneous Nilmanifolds (Geom. Dedicata, Vol. 12, 1982, pp. 337-346). | MR | Zbl
,[Wo1] Curvature in Nilpotent Lie Groups (Proc. Amer. Math. Soc., Vol. 15, 1964, pp. 271-274). | MR | Zbl
,[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
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