SYMPLECTIC RIGIDITY OF GEODESIC-FLOWS ON 2-STEP NILMANIFOLDS

Authors
GORDON CS MAO YP SCHUETH D
Citation
Cs. Gordon et al., SYMPLECTIC RIGIDITY OF GEODESIC-FLOWS ON 2-STEP NILMANIFOLDS, Annales Scientifiques de l'Ecole Normale Superieure, 30(4), 1997, pp. 417-427
Citations number
14
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Annales Scientifiques de l'Ecole Normale Superieure → ACNP
ISSN journal
00129593
Volume
30
Issue
4
Year of publication
1997
Pages
417 - 427
Database
ISI
SICI code
0012-9593(1997)30:4<417:SROGO2>2.0.ZU;2-X
Abstract
We show that if two 2-step Riemannian nilmanifolds have symplectically conjugate geodesic hows, then they must be isometric. By 2-step Riema nnian nilmanifold, we mean a Riemannian manifold of the form (Gamma\N, g), where N is a 2-step nilpotent Lie group, Gamma is a cocompact disc rete subgroup of N, and g is a metric whose pullback to N is left inva riant.