共查询到20条相似文献,搜索用时 15 毫秒
1.
We use the complex and quaternionic hyperbolic versions of Jørgensen's inequality to construct embedded collars about short, simple, closed geodesics in complex and quaternionic hyperbolic manifolds. In general, the width of these collars depend both on the length of the geodesic and on the rotational part of the group element uniformising it. For complex hyperbolic space we are able to use a lemma of Zagier to give an estimate based only on the length. We show that these canonical collars are disjoint from each other and from canonical cusps. We also calculate the volumes of these collars. 相似文献
2.
Richard Chow 《Transactions of the American Mathematical Society》1996,348(5):1757-1769
We show that any finitely generated group quasi-isometric to complex hyperbolic space is a finite extension of a properly discontinuous, cocompact subgroup of the isometry group.
3.
We parametrize the space of isometric immersions of the hyperbolic n -space into the hyperbolic ( n +1)-space by a family of properly chosen (at most) countable n -tuples of real-valued functions. This is an answer to the problem posed by Nomizu in 1973. We also construct a one-parameter family of deformable isometric immersions from the quotient spaces of the hyperbolic 2-plane modulo and some totally discontinuous subgroups of isometries. 相似文献
4.
G. N. Arzhantseva 《Geometriae Dedicata》2001,87(1-3):191-208
We prove that a quasiconvex subgroup H of infinite index of a torsion free word hyperbolic group can be embedded in a larger quasiconvex subgroup which is the free product of H and an infinite cyclic group. Some properties of quasiconvex subgroups of word hyperbolic group are also discussed. 相似文献
5.
Ku Yong Ha Jong Bum Lee Kyung Bai Lee 《Transactions of the American Mathematical Society》2005,357(1):355-383
Let be the quaternionic Heisenberg group of real dimension and let denote the maximal order of the holonomy groups of all infra-nilmanifolds with -geometry. We prove that . As an application, by applying Kim and Parker's result, we obtain that the minimum volume of a -dimensional quaternionic hyperbolic manifold with cusps is at least
6.
Florence Newberger 《Geometriae Dedicata》2003,97(1):215-249
The goal of this paper is to provide a tool, the Global Measure Formula, that will facilitate the study of the limit set of discrete geometrically finite groups of isometries of the rank one symmetric spaces. We consider the shadow of a ball from a fixed reference point onto the boundary, and prove a formula that describes the measure of the shadow in terms of the center of the shadowed ball, generalizing a result from real hyperbolic geometry. 相似文献
7.
本文对Hadamard流形上的等距群Isom(X)进行了研究,得到了几个关于离 散准则和代数收敛性的定理. 相似文献
8.
施云 《高校应用数学学报(A辑)》2016,(1):90-100
定义了四元双曲空间上的链和R-圆,并给出了链在垂直投影下的性质.证明了经过Heisenberg群上固定两点的链的唯一性,R-球的qc-水平性,并给出了R-圆与纯虚R-圆之间的关系. 相似文献
9.
10.
M. Ortega 《Acta Mathematica Hungarica》2002,93(3):225-242
A Riemannian manifold satisfies the axiom of 2-planes if at each point, there are suficiently many totally geodesic surfaces passing through that point. Real hypersurfaces in quaternionic space forms admit nice families of tangent planes, namely, totally real, half-quaternionic and quaternionic. Several definitions of axiom of planes arise naturally when we consider such families of tangent planes. We are able to classify real hypersurfaces in quaternionic space forms satisfying these definitions. 相似文献
11.
In previous work, a probabilistic approach to controlling difficulties of density in hyperbolic space led to a workable notion of optimal density for packings of bodies. In this paper we extend an ergodic theorem of Nevo to provide an appropriate definition of those packings to be considered optimally dense. Examples are given to illustrate various aspects of the density problem, in particular the shift in emphasis from the analysis of individual packings to spaces of packings. 相似文献
12.
13.
In this paper we prove that an n-dimensional compact homogeneous Riemannian manifold isometrically immersed in the hyperbolic space Hn+1 is isometric to a sphere.AMS Subject Classification (1990): 53A07, 53C42, 57S15 相似文献
14.
Jørgensen's inequality gives a necessary condition for a nonelementary two generator group of isometries of hyperbolic space to be discrete. We give analogues of Jørgensen's inequality for nonelementary groups of isometries of complex hyperbolic 2-space generated by two elements, one of which is either loxodromic or boundary elliptic. These results give an improvement over earlier results of Basmajian and Miner. 相似文献
15.
Po-Hsun Hsieh 《Geometriae Dedicata》2003,97(1):93-98
Two bisectors in complex hyperbolic space H
n are called cotranchal if they possess a common slice. We define a natural thing called the prespinal angle between two such bisectors and use it to study the intersection of two such bisectors. 相似文献
16.
A hyperbolic 3-manifold is said to have the spd-property if all its closed geodesics are simple and pairwise disjoint. For a 3-manifold which supports a geometrically finite hyperbolic structure we show the following dichotomy: either the generic hyperbolic structure has the spd-property or no hyperbolic structure has the spd-property. Both cases are shown to occur. In particular, we prove that the generic hyperbolic structure on the interior of a handlebody (or a surface cross an interval) of negative Euler characteristic has the spd-property. Simplicity and disjointness are consequences of a variational result for hyperbolic surfaces. Namely, the intersection angle between closed geodesics varies nontrivially under deformation of a hyperbolic surface. 相似文献
17.
Peng Weiling 《Advances in Applied Clifford Algebras》2007,17(2):273-279
The paper discusses the properties of four-dimensional Minkowski space by using Clifford algebra, then gives the concept of
hyperbolic harmonic function by constructing a system (P4) in the four-dimensional Minkowski space, and obtains several properties and a sufficient and necessary condition for the
solvability of the system (P4) . 相似文献
18.
In this paper we extend to the hyperbolic space results firstly obtainedin Podestà and Spiro (Ann. Global Anal. Geom.
13(2) (1995), 169–184) for compact cohomogeneity, Riemannian manifoldsimmersed as hypersurfaces of the Euclidean space and in Seixas(Ph.D. Thesis, 1996), wherethe complete case was studied. Both works give sufficient conditionsfor the hypersurface to be of revolution. We study cohomogeneity, complete hypersurfaces of the hyperbolic space and prove a similar resultof Seixas (Ph.D. Thesis, 1996), obtaining also a class of nonrotational examples. 相似文献
19.
Igor Belegradek 《Geometriae Dedicata》2003,97(1):45-54
We construct first examples of discrete geometrically finite subgroups of PU(21) which contain parabolic elements, and are isomorphic to surface groups of genus 2. 相似文献
20.
We prove that certain hyperbolic Coxeter groups are separable on their geometrically finite subgroups. 相似文献