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1.
Reeb parallel Ricci tensor for homogeneous real hypersurfaces in complex hyperbolic two‐plane Grassmannians 下载免费PDF全文
In this paper, we introduce the notion of Reeb parallel Ricci tensor for homogeneous real hypersurfaces in complex hyperbolic two‐plane Grassmannians which has a remarkable geometric structure as a Hermitian symmetric space of rank 2. By using a new method of simultaneous diagonalizations, we give a complete classification for real hypersurfaces in complex hyperbolic two‐plane Grassmannians with the Reeb parallel Ricci tensor. 相似文献
2.
Dimitrios E. Kalikakis 《Transactions of the American Mathematical Society》2005,357(7):2829-2841
The notion of a saddle surface is well known in Euclidean space. In this work we extend the idea of a saddle surface to geodesically connected metric spaces. We prove that any solution of the Dirichlet problem for the Sobolev energy in a nonpositively curved space is a saddle surface. Further, we show that the space of saddle surfaces in a nonpositively curved space is a complete space in the Fréchet distance. We also prove a compactness theorem for saddle surfaces in spaces of curvature bounded from above; in spaces of constant curvature we obtain a stronger result based on an isoperimetric inequality for a saddle surface. These results generalize difficult theorems of S.Z. Shefel' on compactness of saddle surfaces in a Euclidean space.
3.
Eric L. Swenson 《Geometriae Dedicata》1995,57(3):297-303
LetX be a negatively curved (Gromov hyperbolic) space. We construct a bound on dim X when a group of isometries acts cocompactly onX. We construct an example of a negatively curved space with infinite-dimensional boundary. 相似文献
4.
We introduce the notion of the lightcone Gauss–Kronecker curvature for a spacelike submanifold of codimension two in Minkowski
space, which is a generalization of the ordinary notion of Gauss curvature of hypersurfaces in Euclidean space. In the local
sense, this curvature describes the contact of such submanifolds with lightlike hyperplanes. We study geometric properties
of such curvatures and show a Gauss–Bonnet type theorem. As examples we have hypersurfaces in hyperbolic space, spacelike
hypersurfaces in the lightcone and spacelike hypersurfaces in de Sitter space. 相似文献
5.
We construct examples of Gromov hyperbolic
Coxeter groups of arbitrarily large dimension.
We also extend Vinbergs theorem to show that if a Gromov
hyperbolic Coxeter group is a virtual Poincaré duality group
of dimension n,
then n 61.Coxeter groups acting on their associated complexes have been extremely
useful source of examples and insight into nonpositively curved spaces
over last several years. Negatively curved (or Gromov hyperbolic)
Coxeter groups were much more elusive. In particular their existence in
high dimensions was in doubt.In 1987 Gabor Moussong [M] conjectured that there is a universal bound on
the virtual cohomological dimension of any Gromov hyperbolic Coxeter group.
This question was also raised by Misha Gromov [G] (who thought that perhaps
any construction of high dimensional negatively curved spaces requires
nontrivial number theory in the guise of arithmetic groups in an essential
way), and by Mladen Bestvina [B2].In the present paper we show that high dimensional Gromov hyperbolic Coxeter
groups do exist, and we construct them by geometric or group theoretic but
not arithmetic means. 相似文献
6.
Frank Neumann 《Journal of Pure and Applied Algebra》1999,140(3):205
We prove a collapse theorem for the Eilenberg–Moore spectral sequence and as an application we show that under certain conditions the cohomology of a homogeneous space of a connected finite loop space with a maximal rank torsion free subgroup is concentrated in even degrees and torsionfree, generalizing classical theorems for compact Lie groups of Borel and Bott. 相似文献
7.
Clark Butler 《Israel Journal of Mathematics》2018,227(1):27-61
We show that any measurable solution of the cohomological equation for a Hölder linear cocycle over a hyperbolic system coincides almost everywhere with a Hölder solution. More generally, we show that every measurable invariant conformal structure for a Hölder linear cocycle over a hyperbolic system coincides almost everywhere with a continuous invariant conformal structure. We also use the main theorem to show that a linear cocycle is conformal if none of its iterates preserve a measurable family of proper subspaces of Rd. We use this to characterize closed negatively curved Riemannian manifolds of constant negative curvature by irreducibility of the action of the geodesic flow on the unstable bundle. 相似文献
8.
Tullia Dymarz 《Geometric And Functional Analysis》2010,19(6):1650-1687
In this paper we provide the final steps in the proof of quasi-isometric rigidity of a class of non-nilpotent polycyclic groups.
To this end, we prove a rigidity theorem on the boundaries of certain negatively curved homogeneous spaces and combine it
with work of Eskin–Fisher–Whyte and Peng on the structure of quasiisometries of certain solvable Lie groups. 相似文献
9.
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
10.
We show that the open unit ball of the space of operators from a finite-dimensional Hilbert space into a separable Hilbert space (we call it “operator ball”) has a restricted form of normal structure if we endow it with a hyperbolic metric (which is an analogue of the standard hyperbolic metric on the unit disc in the complex plane). We use this result to get a fixed point theorem for groups of biholomorphic automorphisms of the operator ball. The fixed point theorem is used to show that a bounded representation in a separable Hilbert space which has an invariant indefinite quadratic form with finitely many negative squares is unitarizable (equivalent to a unitary representation). We apply this result to find dual pairs of invariant subspaces in Pontryagin spaces. In Appendix A we present results of Itai Shafrir about hyperbolic metrics on the operator ball. 相似文献
11.
Curved flats,pluriharmonic maps and constant curvature immersions into pseudo-Riemannian space forms 总被引:1,自引:0,他引:1
David Brander 《Annals of Global Analysis and Geometry》2007,32(3):253-275
We study two aspects of the loop group formulation for isometric immersions with flat normal bundle of space forms. The first
aspect is to examine the loop group maps along different ranges of the loop parameter. This leads to various equivalences
between global isometric immersion problems among different space forms and pseudo-Riemannian space forms. As a corollary,
we obtain a non-immersibility theorem for spheres into certain pseudo-Riemannian spheres and hyperbolic spaces. The second
aspect pursued is to clarify the relationship between the loop group formulation of isometric immersions of space forms and
that of pluriharmonic maps into symmetric spaces. We show that the objects in the first class are, in the real analytic case,
extended pluriharmonic maps into certain symmetric spaces which satisfy an extra reality condition along a totally real submanifold.
We show how to construct such pluriharmonic maps for general symmetric spaces from curved flats, using a generalised DPW method.
相似文献
12.
We consider iso-Huygens deformations of homogeneous hyperbolic Gindikin operators related to a special cone of rank ${\text{3}}$ . The deformations are carried out with the use of Stellmacher--Lagnese and Calogero--Moser potentials. Using the notion of gauge equivalence of operators and the algebraic method of intertwining operators, we write out the fundamental solutions of the deformed operators in closed form and give sufficient conditions for the Huygens principle to hold for these operators in the strengthened or ordinary form. 相似文献
13.
We introduce the notion of geometrical engagement for actions of semisimple Lie groups and their lattices as a concept closely
related to Zimmer's topological engagement condition. Our notion is a geometrical criterion in the sense that it makes use
of Riemannian distances. However, it can be used together with the foliated harmonic map techniques introduced in [8] to establish
foliated geometric superrigidity results for both actions and geometric objects. In particular, we improve the applications
of the main theorem in [9] to consider nonpositively curved compact manifolds (not necessarily with strictly negative curvature).
We also establish topological restrictions for Riemannian manifolds whose universal cover have a suitable symmetric de Rham
factor (Theorem B), as well as geometric obstructions for nonpositively curved compact manifolds to have fundamental groups
isomorphic to certain groups build out of cocompact lattices in higher rank simple Lie groups (Corollary 4.5).
Received: October 22, 1997 相似文献
14.
We study horo-tight immersions of manifolds into hyperbolic spaces. The main result gives several characterizations of horo-tightness of spheres, answering a question proposed by Cecil and Ryan. For instance, we prove that a sphere is horo-tight if and only if it is tight in the hyperbolic sense. For codimension bigger than one, it follows that horo-tight spheres in hyperbolic space are metric spheres. We also prove that horo-tight hyperspheres are characterized by the property that both of its total absolute horospherical curvatures attend their minimum value. We also introduce the notion of weak horo-tightness: an immersion is weak horo-tight if only one of its total absolute curvature attends its minimum. We prove a characterization theorem for weak horo-tight hyperspheres. 相似文献
15.
We generalize the notion of fixed point homogeneous isometric group actions to the context of singular Riemannian foliations. We find that in some cases, positively curved manifolds admitting these so-called point leaf maximal SRF's are diffeo/homeomorphic to compact rank one symmetric spaces. In all cases, manifolds admitting such foliations are cohomology CROSSes or finite quotients of them. Among non-simply connected manifolds, we find examples of such foliations which are non-homogeneous. 相似文献
16.
Benoît Kloeckner 《Mathematische Annalen》2010,347(4):951-961
Any nonpositively curved symmetric space admits a topological compactification, namely the Hadamard compactification. For
rank 1 spaces, this topological compactification can be endowed with a differentiable structure such that the action of the
isometry group is differentiable. Moreover, the restriction of the action on the boundary leads to a flat model for some geometry
(conformal, CR or quaternionic CR depending of the space). One can ask whether such a differentiable compactification exists
for higher rank spaces, hopefully leading to some knew geometry to explore. In this paper we answer negatively. 相似文献
17.
Z. Sela 《Geometric And Functional Analysis》1997,7(3):561-593
We borrow the Jaco-Shalen-Johannson notion of characteristic sub-manifold from 3-dimensional topology to study cyclic splittings
of torsion-free (Gromov) hyperbolic groups and finitely generated discrete groups in rank 1 Lie groups. Our JSJ canonical
decomposition is a fundamental object for studying the dynamics of individual automorphisms and the automorphism group of
a torsion-free hyperbolic group and a key tool in our approach to the isomorphism problem for these groups [S3]. For discrete
groups in rank 1 Lie groups, the JSJ canonical decomposition serves as a basic object for understanding the geometry of the
space of discrete faithful representations and allows a natural generalization of the Teichmüller modular group and the Riemann
moduli space for these discrete groups.
Submitted: September 1996, revised version: April 1997 相似文献
18.
In dynamical systems theory, a standard method for passing from discrete time to continuous time is to construct the suspension
flow under a roof function. In this paper, we give conditions under which statistical laws, such as the central limit theorem
and almost sure invariance principle, for the underlying discrete time system are inherited by the suspension flow. As a consequence,
we give a simpler proof of the results of Ratner (1973) and recover the results of Denker and Philipp (1984) for Axiom A flows.
Morcover, we obtain several new results for nonuniformly and partially hyperbolic flows, including frame flows on negatively
curved manifolds satisfying a pinching condition. 相似文献
19.
20.
We consider distribution results for closed orbits of the
partially hyperbolic system: an ergodic toral automorphism Ã
with respect to a (G,
)–extension A. In particular we obtain an analogue of the
Chebotarev theorem in this situation which is an asymptotic
formula for the number of closed orbits of the base
transformation according to how they lift onto the extension
space. To arrive at this result we introduce a cyclic extension
 of A and deduce that  and A is essentially a group extension
and homogeneous extension of à respectively. This observation of
a group extension is similar to the setting previously studied
by Parry & Pollicott and using the prime orbit theorem of
Waddington we then derive at an auxiliary result for the group
extension analogoues to Parry & Pollicott. Finally we relate
this auxiliary result to the homogeneous extension by resorting
to the work of Noorani & Parry. 相似文献