共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
Xiaobao Zhu 《偏微分方程(英文版)》2015,28(1):39-46
In this paper, we establish a singular Trudinger-Moser inequality for the whole hyperbolic space $$H^n: sup_{u∈W^{1,n}(H^n),∫_{H^n}|∇_H^nu|^ndμ ≤ 1}∫_{H^n}\frac{e^{α|u|\frac{n}{n-1}}-Σ^{n-2}_{k=0}\frac{α^k|u|^\frac{nk}{n-1}}{k!}}{ρ^β}dμ‹∞ ⇔ \frac{α}{α_n}+\frac{β}{n} ≤ 1,$$ where α>0,α ∈ [0,n), ρ and dμ are the distance function and volume element of $H^n$ respectively. 相似文献
3.
讨论了双曲空间中Laplace-Beltrami方程的一个带位移的边值问题.首先将双曲空间中的Laplace-Beltrami方程的解转化为Clifford分析中的超正则函数.然后给出了超正则函数的Plemelj公式并讨论了相关奇异积分算子的性质,最后利用积分方程的方法和压缩不动点原理证明了Laplace-Beltrami方程的一个带位移的边值问题的解的存在性和唯一性. 相似文献
4.
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
5.
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
6.
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
7.
Quasi—Einstein Hypersurfaces in a Hyperbolic Space 总被引:1,自引:0,他引:1
§1. IntroductionLetRijbethecomponentsofRiccitensorofann-dimensionalRiemannianmanifoldM.IfRij=Agij Bξiξj, (i,j=1,2,…,n)(1.1)whereξisanunitvectorfield,thenMiscalledaquasi-EinsteinmanifoldanddenotedbyQE(ξ).Ifξisanisotropicvectorfield,thenMiscalledageneralizedquasi-Einsteinmanifold.Intheequality(1.1),AandBarescalarfunctions.WeknowQE(ξ)manifoldisEinsteinwhenB≡0.Especially,if〈ξ,ξ〉=e=±1,thenQE(ξ)iscalledanormalquasi-Einsteinmani-fold.Itiseasytoknowfrom[1]and[2]:Rij=R-Tn-1… 相似文献
8.
本文证明了双曲空间中的共形平坦极小超曲面必为旋转超曲面或由一些旋转超曲面片用全测地超曲面片粘合而成.将这结果与王新民及许志才的一个已发表定理相组合,推广了Blair关于推广悬链面的一个定理. 相似文献
9.
Po-Hsun Hsieh 《Geometriae Dedicata》2003,97(1):99-113
We study a nonidentity transvection (i.e. (strictly) hyperbolic isometry) or nonidentity Heisenberg translation f of complex hyperbolic space H
n and a Dirichlet polyhedron P of the cyclic group f. We have four main results: (a) If z & in H
n and the axis of a nonidentity transvection are not complex collinear, then, roughly speaking, any two distinct 'naturally arising' geodesics passing through z are not complex collinear. (b) If g is also a transvection or Heisenberg translation of H
n and z & in H
n such that f(z)=g(z) and f
–1(z)=g
–1(z), then f=g. (c) We classify all this kind of polyhedra up to congruence in H
n. (d) We obtain an equivalent condition for P to be cospinal (which means that the complex spines of the two sides of P coincide) in terms of the distance of the spines of the two sides of P. 相似文献
10.
11.
Rafael López 《Geometriae Dedicata》2006,119(1):35-47
We deposit a prescribed amount of liquid on an umbilical hypersurface Π of the hyperbolic space
. Under the presence of a uniform gravity vector field directed towards Π, we seek the shape of such a liquid drop in a state of equilibrium of the mechanical system. The liquid-air interface in then modeled by a hypersurface under the condition that its mean curvature is a function of the distance from Π, together with the fact that the angle that makes with Π along its boundary is constant. We show that the hypersurface is rotational symmetric with respect to a geodesic orthogonal to Π. We extend this result to other configurations, for example, liquid bridges trapped between two umbilical hypersurfaces. Finally, we obtain a result which says that, under some assumptions on the mean curvature, an embedded hypersurface inherits a certain symmetry from its boundary.Partially supported by MEC-FEDER Grant no. MTM2004-00109. 相似文献
12.
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
13.
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.
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.
双曲空间Hn+p(-1)中具常数量曲率的完备子流形 总被引:3,自引:0,他引:3
设Mn是Hn p(-1)中具有常标准数量曲率的n维完备子流形,本文证明了这种完备子流形的某些内蕴刚性定理和分类定理,并对超曲面的情形进行了研究. 相似文献
16.
Boris Rubin 《Advances in Mathematics》2002,170(2):206-223
New pointwise inversion formulae are obtained for the d-dimensional totally geodesic Radon transform on the n-dimensional real hyperbolic space, 1dn−1, in terms of polynomials of the Laplace–Beltrami operator and intertwining fractional integrals. Similar results are established for hyperbolic cosine and sine transforms. 相似文献
17.
Let (X
i
d
i
), i=1,2, be proper geodesic hyperbolic metric spaces. We give a general construction for a 'hyperbolic product' X
1×
h
X
2 which is itself a proper geodesic hyperbolic metric space and examine its boundary at infinity. 相似文献
18.
Jorge Herbert S. De Lira 《Geometriae Dedicata》2002,93(1):11-23
The existence is proved of radial graphs with constant mean curvature in the hyperbolic space H
n+1 defined over domains in geodesic spheres of H
n+1 whose boundary has positive mean curvature with respect to the inward orientation. 相似文献
19.
Yu Xuegang 《Advances in Applied Clifford Algebras》2000,10(1):49-60
The hyperbolic complex space is one class of non-Euclidean spaces with continuous singular points. It corresponds with Minkowski
space, and it has the characteristic that the space-time direction is different in nature. Regard the hyperbolic complex space
as original spaces. We can abstract a class of the hyperbolic inner product space and the hyperbolic Hilbert space. 相似文献
20.
In this paper, we consider a nonlocal problem with integral conditions for the quasilinear hyperbolic equation in a rectangular domain. The existence and uniqueness of the generalized solution are established. 相似文献