共查询到20条相似文献,搜索用时 0 毫秒
1.
Mohamed Deffaf Karin Melnick Abdelghani Zeghib 《Geometric And Functional Analysis》2008,18(2):463-488
The above title is the same, but with “semisimple” instead of “simple,” as that of a notice by Nadine Kowalsky. There, she
announced many theorems on the subject of actions of simple Lie groups preserving a Lorentz structure. Unfortunately, she
published proofs for essentially only half of the announced results before her premature death. Here, using a different, geometric
approach, we generalize her results to the semisimple case, and give proofs of all her announced results.
Received: May 2006, Revision: February 2007, Accepted: March 2007 相似文献
2.
Scot Adams 《Geometriae Dedicata》2003,98(1):1-45
If a topological group G acts on a topological space X, then we say that the action is orbit nonproper provided that, for some xX, the orbit map ggx:GX is nonproper. We consider the problem of classifying the connected, simply connected real Lie groups G admitting a locally faithful, orbit nonproper, isometric action on a connected Lorentz manifold. In an earlier paper, we found three collections of groups such that G admits such an action iff G is in one of the three collections. In another paper, we effectively described the first collection. In this paper, we show that the second collection contains a small, effectively described collection of groups, and, aside from those, it is contained in the union of the first and third collections. Finally, in a third paper, we effectively describe the third collection, thus solving the stated problem. 相似文献
3.
Scot Adams 《Geometriae Dedicata》2004,105(1):1-12
We give an alternate proof of N. Kowalsky's theorem describing the collection of connected simple Lie groups with finite center
which admit a nontrivial, nonproper action by isometries of a connected Lorentz manifold. 相似文献
4.
Harald Biller 《Geometriae Dedicata》2000,83(1-3):273-312
We establish sharp upper bounds for the dimensions of compact groups which act effectively on finite-dimensional compact generalized quadrangles with four-dimensional point rows. These bounds are attained, or indeed approached, only for explicitly known actions of Lie groups on Moufang quadrangles. 相似文献
5.
VALERY MARENICH 《Geometriae Dedicata》1997,66(2):175-185
We obtain equations of geodesic lines in Heisenberg groups H2n+1and prove that the ideal boundary of the Heisenberg group H2n+1is a sphere S2n-1with a natural CR-structure and corresponding Carnot-Carathéodory metric, i.e. it is a one-point compactification of the Heisenberg group H2n-1of the next dimension in a row. 相似文献
6.
We study the action of a connected noncompact simple Lie group G on a connected finite volume pseudo-Riemannian manifold M. Our main result provides a geometric splitting of the metric on such M that involves natural metrics on G. For suitable G such splitting is a warped product. For any G the splitting turns out to be a direct product in the ergodic case. 相似文献
7.
Toshiyuki Kobayashi 《Acta Appl Math》2002,73(1-2):115-131
Isometric actions of discrete groups are not always properly discontinuous for pseudo-Riemannian manifolds. This short exposition gives an up-to-date survey of some of the basic questions about discontinuous groups for pseudo-Riemannian homogeneous spaces, on which a rapid development has been made since late 1980s.The first half includes an elementary geometric motivation, the Calabi–Markus phenomenon, the discontinuous dual, and deformation. These topics are rebuilt on a criterion of properly discontinuous actions on homogeneous spaces of reductive groups, obtained by Kobayashi [Math. Ann. 1989] and generalized independently by Benoist [Ann. Math. 1996] and Kobayashi [J. Lie Theory 1996].The second half discusses the existence problem of compact Clifford–Klein forms of pseudo-Riemannian homogeneous spaces, for which many new methods from different areas have been recently employed. We examine these various approaches in some typical cases. We also point out that Zimmer's examples on SL(n)/SL(m) [J. Amer. Math. Soc. 1994] and Shalom's examples on SL(n)/SL(2) [Ann. Math. 2000] are readily obtained as special cases of Kobayashi's criterion [Duke Math. J. 1992], where the former uses ergodic theory and restrictions of unitary representations, respectively, while the latter uses cohomologies of discrete groups.The article also explains some open problems and conjectures. 相似文献
8.
Andrzej Szczepański 《Geometriae Dedicata》2006,120(1):111-118
We present about twenty conjectures, problems and questions about flat manifolds. Many of them build the bridges between the flat world and representation theory of the finite groups, hyperbolic geometry and dynamical systems.
In memory of Charles B. Thomas 相似文献
9.
我们对复Banach空间上的可数sofic群的等距线性作用提出了一种新的维数,推广了复Banach空间上的可数顺从群的等距线性作用的Voiculescu维数,并且在可数sofic群的情形回答了Gromov的一个问题. 相似文献
10.
V. G. Bardakov 《Acta Appl Math》2005,85(1-3):41-48
In this paper we prove that the braid group Bn(S2) of 2-sphere, mapping class group M(0,n) of the n-punctured 2-sphere and the braid group B3(P2) of the projective plane are linear.
Partially supported by the Russian Foundation for Basic Research (grant number 02-01-01118).Mathematics Subject Classifications (2000) 20F28, 20F36, 20G35. 相似文献
11.
Let Heis
2n+1 be the Heisenberg group of dimension 2n + 1 and M an infra-nilmanifold with Heis
2n+1-geometry. The fundamental group of M contains a cocompact lattice of Heis
2n+1 with index bounded above by a universal constant I
n+1, i.e., I
n+1 is the maximal order of the holonomy groups. We prove that I
3 = 24. As an application we give an estimate for the volumes of finite volume non-compact complex hyperbolic 3-manifolds. 相似文献
12.
在本文中,我们利用李群及其表示理论作为主要工具, 讨论了紧黎曼对称空间到Grassmann 流形的等变等距极小浸入问题. 相似文献
13.
本文求得了H型群上次Laplace算子的基本解,并以此为基础,给出了平均值公式、Hardy型不等式、不确定原理及唯一延拓性. 相似文献
14.
Bin QIAN 《数学年刊B辑(英文版)》2010,31(3):305-314
The author obtains sharp gradient estimates for the heat kernels in two kinds of higher dimensional Heisenberg groups -- the non-isotropic Heisenberg group and the Heisenberg type group Hn,m. The method used here relies on the positive property of the Bakry-Emery curvature F2 on the radial functions and some associated semigroup technics. 相似文献
15.
Yongyang JIN 《数学年刊B辑(英文版)》2008,29(5):567-574
The author obtains some weighted Hardy-type inequalities on H-type groups and anisotropic Heisenberg groups. These inequalities generalize some recent results due to N. Garofalo, E. Lanconelli, I. Kombe and P. Niu et al. 相似文献
16.
Pinched流形上等距群的几个性质 总被引:2,自引:0,他引:2
本文建立了Pinched流形X上等距群M(X)中的Jorgensen型不等式;证得了M(X)中非初等群的一个几何特征,得到了M(X)中子群的两个离散准则。 相似文献
17.
Let G = SL(n, ?) (or, more generally, let G be a connected, noncompact, simple Lie group). For any compact Lie group K, it is easy to find a compact manifold M, such that there is a volume-preserving, connection-preserving, ergodic action of G on some smooth, principal K-bundle P over M. Can M can be chosen independent of K? We show that if M = H/Λ is a homogeneous space, and the action of G on M is by translations, then P must also be a homogeneous space H′Λ′. Consequently, there is a strong restriction on the groups K that can arise over this particular M. 相似文献
18.
Yves Benoist 《Geometriae Dedicata》2002,89(1):177-241
For any symplectic action of a compact connected group on a compact connected symplectic manifold, we show that the intersection
of the Weyl chamber with the image of the moment map is a closed convex polyhedron. This extends Atiyah–Guillemin–Sternberg–Kirwan's
convexity theorems to non-Hamiltonian actions. As a consequence, we describe those symplectic actions of a torus which are
coisotropic (or multiplicity free), i.e. which have at least one coisotropic orbit: they are the product of an Hamiltonian
coisotropic action by an anhamiltonian one. The Hamiltonian coisotropic actions have already been described by Delzant thanks
to the convex polyhedron. The anhamiltonian coisotropic actions are actions of a central torus on a symplectic nilmanifold.
This text is written as an introduction to the theory of symplectic actions of compact groups since complete proofs of the
preliminary classical results are given.
An erratum to this article is available at . 相似文献
19.
A characterization of the maximal abelian sub-algebras of matrix algebras that are normalized by the canonical representation of a finite Heisenberg group is given. Examples are constructed using a classification result for finite Heisenberg groups. 相似文献
20.
设L=-△_(H~n)+V是Heisenberg群H~n上的Schr(o|¨)dinger算子,其中△_(H~n)为H~n上的次Laplacian,V≠0为满足逆H(o|¨)lder不等式的非负函数.本文研究H~n上Riesz位势I_α~L=L~(-α/2)在Campanato型空间A_L~β和Hardy型空间H_L~p上的某些性质. 相似文献