Symplectic rigidity of geodesic flows on two-step nilmanifolds1

DOI10.1016/S0012-9593(97)89927-2zbMath0897.53033OpenAlexW2048776354MaRDI QIDQ4350891

Dorothee Schueth, Yiping Mao, Carolyn S. Gordon

Publication date: 20 October 1998

Published in: Annales Scientifiques de l’École Normale Supérieure (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=ASENS_1997_4_30_4_417_0

zbMATH Keywords

symplectic rigidity2-step nilmanifoldsgeodesic conjugacy

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Geodesics in global differential geometry (53C22) Geodesic flows in symplectic geometry and contact geometry (53D25) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (6)

The moduli space of six-dimensional two-step nilpotent Lie algebras ⋮ Integrability of geodesic flows and isospectrality of Riemannian manifolds ⋮ The minimal marked length spectrum of Riemannian two-step nilmanifolds ⋮ An application of Lie groupoids to a rigidity problem of 2-step nilmanifolds ⋮ The geodesic flow on nilmanifolds associated to graphs ⋮ Continuous families of Riemannian manifolds, isospectral on functions but not on 1-forms

Cites Work

• Le spectre marqué des longueurs des surfaces à courbure négative. (The spectrum marked by lengths of surfaces with negative curvature)
• Rigidity for surfaces of non-positive curvature
• Isospectral deformations of compact solvmanifolds
• The marked length-spectrum of a surface of nonpositive curvature
• Lie groups and Lie algebras III. Structure of Lie groups and Lie algebras. Transl. from the Russian by V. Minachin
• Comparisons of Laplace spectra, length spectra and geodesic flows of some Riemannian manifolds
• Microlocal Analysis of Some Isospectral Deformations
• Geometry of $2$-step nilpotent groups with a left invariant metric
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