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A nonlinear extension of the Borel density theorem: Applications to invariance of geometric structures and to smooth orbit equivalence
Author(s):
Alessandra
Iozzi
Journal:
Bull. Amer. Math. Soc.
23
(1990),
115-120.
MSC (1985):
Primary 22DXX, 22E40, 28DXX, 53C35, 57R30, 57S20
MathSciNet review:
1021792
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References:
- [Be] D. Benardete, Topological equivalence of flows on homogeneous spaces and divergence of one-parameter subgroups of Lie groups, Trans. Amer. Math. Soc. 306(1988), 499-528. MR 933304
- [Bo] A. Borel, Density properties for certain subgroups of semisimple Lie groups without compact factors, Ann. of Math. 72 (1960), 179-188. MR 123639
- [Ch] C. Chevalley, Théorie des groupes de Lie, II: groupes algébréques, Hermann, Paris, 1951. MR 51242
- [M] C. C. Moore, Ergodicity of flows on homogeneous spaces, Amer. J. Math. 88(1966), 154-178. MR 193188
- [PZ] P. Pansu and R. J. Zimmer, Rigidity of locally homogenous metrics of negative curvature on the leaves of a foliation, Israel J. Math. 68 (1989), 56-62. MR 1035880
- [Wa] N. R. Wallach, Asymptotic expansions of generalized matrix entries of representations of real reductive groups, Lecture Notes in Math., vol. 1024, Springer-Verlag, New York, 1983, 287-369. MR 727854
- [Wi 1 ] D. Witte, Rigidity of some translations on homogeneous spaces, Bull. Amer. Math. Soc. 12, 117-119. MR 766966
- [Wi 2] D. Witte, Topological equivalence of foliations of homogeneous spaces, Trans. Amer. Math. Soc. 317 (1990), 143-166. MR 942428
- [Z 1] R. J. Zimmer, Ergodic theory and semisimple groups, Birkhäuser, Boston, 1984. MR 776417
- [Z 2] R. J. Zimmer, Lattice in semisimple groups and invariant geometric structures on compact manifolds, in Discrete groups in geometry and analysis, (R. Howe, editor), Birkhäuser, Boston, 1987. MR 900826
- [Z 3] R. J. Zimmer, On the automorphism groups of a compact Lorentz manifold and other geometric manifolds, Invent. Math. 83 (1986), 411-424. MR 827360
- [Z 4] R. J. Zimmer, Orbit equivalence and rigidity of ergodic actions of Lie groups, Ergodic Theory Dynamical Systems 1 (1986), 237-253. MR 661822
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22DXX, 22E40, 28DXX, 53C35, 57R30, 57S20
Additional Information:
DOI:
10.1090/S0273-0979-1990-15915-4
PII:
S 0273-0979(1990)15915-4
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