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M. Tavares 《Topology and its Applications》2011,158(4):636-641
We study Anosov actions of nilpotent Lie groups on closed manifolds. Our main result is a generalization to the nilpotent case of a classical theorem by J.F. Plante in the 70's. More precisely, we prove that, for what we call a good Anosov action of a nilpotent Lie group on a closed manifold, if the non-wandering set is the entire manifold, then the closure of stable strong leaves coincide with the closure of the strong unstable leaves. This implies the existence of an equivariant fibration of the manifold onto a homogeneous space of the Lie group, having as fibers the closures of the leaves of the strong foliation. 相似文献
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Morris W. Hirsch 《Journal of Fixed Point Theory and Applications》2011,10(2):219-232
Necessary or sufficient conditions are presented for the existence of various types of actions of Lie groups and Lie algebras on manifolds. 相似文献
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Abdelghani Zeghib 《Mathematische Zeitschrift》1998,227(2):245-262
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André Diatta 《Geometriae Dedicata》2008,133(1):83-94
We investigate contact Lie groups having a left invariant Riemannian or pseudo-Riemannian metric with specific properties
such as being bi-invariant, flat, negatively curved, Einstein, etc. We classify some of such contact Lie groups and derive
some obstruction results to the existence of left invariant contact structures on Lie groups.
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Maria Gordina 《Journal of Functional Analysis》2005,227(2):245-272
We describe the exponential map from an infinite-dimensional Lie algebra to an infinite-dimensional group of operators on a Hilbert space. Notions of differential geometry are introduced for these groups. In particular, the Ricci curvature, which is understood as the limit of the Ricci curvature of finite-dimensional groups, is calculated. We show that for some of these groups the Ricci curvature is -∞. 相似文献
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In this paper we introduce the notion of symplectically asystatic Hamiltonian action on a Kahler manifold. In the algebraic
setting we prove that if a complex linear group G acts on a Kahler manifold in a symplectically asystatic fashion, then the
G-orbits are spherical. Finally, we give the complete classification of symplectically asystatic irreducible representations. 相似文献
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Shahar Mozes 《Inventiones Mathematicae》1995,119(1):399-399
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Shahar Mozes 《Inventiones Mathematicae》1992,107(1):235-241
Summary We show that for Lie groups whose adjoint representation reflects their topology, mixing implies mixing of all orders. In particular we prove that mixing actions of a semisimple Lie group are mixing of all orders, answering a conjecture of B. Marcus.Oblatum 6-VIII-1990 & 4-IV-1991Sponsored in part by the Edmund Landau Center for research in Mathematical Analysis supported by the Minerva Foundation (Federal Republic of Germany) 相似文献
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The degenerate semi-Riemannian geometry of a Lie group is studied. Then a naturally reductive homogeneous semi-Riemannian space is obtained from the Lie group in a natural way. 相似文献
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Burkhard Wilking 《Mathematische Annalen》2000,317(2):195-237
We establish analogs of the three Bieberbach theorems for a lattice in a semidirect product where is a connected, simply connected solvable Lie group and is a compact subgroup of its automorphism group. We first prove that the action of on is metrically equivalent to an action of on a supersolvable Lie group. The latter is shown to be determined by itself up to an affine diffeomorphism. Then we characterize these lattices algebraically as polycrystallographic groups. Furthermore, we realize any polycrystallographic group as a lattice in a semidirect product with being a finite group whose order is bounded by a constant only depending on the dimension of . This generalization of the first Bieberbach theorem is used to obtain a partial generalization of the third one as well. Finally we show for any torsion free closed subgroup that the quotient is the total space of a vector bundle over a compact manifold B, where B is the quotient of a solvable Lie group by a torsion free polycrystallographic group. Received: 27 August 1999 相似文献
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Peter W. Michor 《Proceedings of the American Mathematical Society》1996,124(5):1633-1642
A section of a Riemannian -manifold is a closed submanifold which meets each orbit orthogonally. It is shown that the algebra of -invariant differential forms on which are horizontal in the sense that they kill every vector which is tangent to some orbit, is isomorphic to the algebra of those differential forms on which are invariant with respect to the generalized Weyl group of , under some condition.
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Using groupoid S1-central extensions, we present, for a compact simple Lie group G, an infinite dimensional model of S1-gerbe over the differential stack G/G whose Dixmier–Douady class corresponds to the canonical generator of the equivariant cohomology HG3(G). To cite this article: K. Behrend et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003). 相似文献