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1.
Lisa DeMeyer 《manuscripta mathematica》2001,105(3):283-310
We study the density of closed geodesics property on 2-step nilmanifolds Γ\N, where N is a simply connected 2-step nilpotent Lie group with a left invariant Riemannian metric and Lie algebra ?, and Γ is a lattice
in N. We show the density of closedgeodesics property holds for quotients of singular, simply connected, 2-step nilpotent Lie
groups N which are constructed using irreducible representations of the compact Lie group SU(2).
Received: 8 November 2000 / Revised version: 9 April 2001 相似文献
2.
Mohammed Guediri 《Mathematische Zeitschrift》2002,239(2):277-291
In [19], Tipler has shown that a compact spacetime having a regular globally hyperbolic covering space with compact Cauchy
surfaces necessarily contains a closed timelike geodesic. The restriction to compact spacetimes with just regular globally
hyperbolic coverings (i.e., the Cauchy surfaces are not required to be compact) is still an open question. Here, we shall
answer this question negatively by providing examples of compact flat Lorentz space forms without closed timelike geodesics,
and shall give some criterion for the existence of such geodesics. More generally, we will show that in a compact spacetime
having a regular globally hyperbolic covering, each free timelike homotopy class determined by a central deck transformation
must contain a closed timelike geodesic. Whether or not a compact flat spacetime contains closed nonspacelike geodesics is,
as far as we know, an open question. We shall answer this question affirmatively. We shall also introduce the notion of timelike
injectivity radius for a spacetime relative to a free timelike homotopy class and shall show that it is finite whenever the
corresponding deck transformation is central.
Received: 9 November 1999; in final form: 19 September 2000 / Published online: 25 June 2001 相似文献
3.
Index estimates for strongly indefinite functionals, periodic orbits and homoclinic solutions of first order Hamiltonian systems 总被引:3,自引:0,他引:3
Alberto Abbondandolo Juan Molina 《Calculus of Variations and Partial Differential Equations》2000,11(4):395-430
We improve Benci and Rabinowitz's Linking theorem for strongly indefinite functionals, giving estimates for a suitably defined
relative Morse index of critical points. Such abstract result is applied to the existence problem of periodic orbits and homoclinic
solutions of first order Hamiltonian systems in cases where the Palais-Smale condition does not hold.
Received January 27, 1999 / Accepted January 14, 2000 / Published online July 20, 2000 相似文献
4.
Miguel Angel Javaloyes Paolo Piccione 《Calculus of Variations and Partial Differential Equations》2008,33(4):439-462
We introduce the notion of spectral flow along a periodic semi-Riemannian geodesic, as a suitable substitute of the Morse
index in the Riemannian case. We study the growth of the spectral flow along a closed geodesic under iteration, determining
its asymptotic behavior.
M. A. J. is sponsored by Fapesp; P. P. is partially sponsored by CNPq. 相似文献
5.
Vladimir S. Matveev 《Inventiones Mathematicae》2003,151(3):579-609
We show that if all geodesics of two non-proportional metrics on a closed manifold coincide (as unparameterized curves), then
the manifold has a finite fundamental group or admits a local-product structure. This implies that, if the manifold admits
a metric of negative sectional curvature, then two metrics on the manifold have the same geodesics if and only if they are
proportional.
Oblatum 18-IV-2002 & 12-VIII-2002?Published online: 18 December 2002 相似文献
6.
Stephanie Halbeisen 《manuscripta mathematica》2000,103(2):169-182
The tangent cones of an inner metric Alexandrov space with finite Hausdorff dimension and a lower curvature bound are always inner metric spaces with nonnegative curvature. In this paper we construct an infinite-dimensional inner metric Alexandrov
space of nonnegative curvature which has in one point a tangent cone whose metric is not an inner metric.
Received: 20 October 1999 / Revised version: 8 May 2000 相似文献
7.
Miguel Angel Javaloyes Levi Lopes de Lima Paolo Piccione 《Mathematische Zeitschrift》2008,260(2):277-303
Following the lines of Bott in (Commun Pure Appl Math 9:171–206, 1956), we study the Morse index of the iterates of a closed
geodesic in stationary Lorentzian manifolds, or, more generally, of a closed Lorentzian geodesic that admits a timelike periodic
Jacobi field. Given one such closed geodesic γ, we prove the existence of a locally constant integer valued map Λγ on the unit circle with the property that the Morse index of the iterated γ
N
is equal, up to a correction term εγ∈{0,1}, to the sum of the values of Λγ at the N-th roots of unity. The discontinuities of Λγ occur at a finite number of points of the unit circle, that are special eigenvalues of the linearized Poincaré map of γ.
We discuss some applications of the theory. 相似文献
8.
Evangelia Samiou 《manuscripta mathematica》2002,107(1):101-110
We construct a family of simply connected 2-step nilpotent Lie groups of higher rank such that every geodesic lies in a flat.
These are as Riemannian manifolds irreducible and arise from real representations of compact Lie algebras. Moreover we show
that groups of Heisenberg type do not even infinitesimally have higher rank.
Received: 2 July 2001 / Revised version: 19 October 2001 相似文献
9.
Gen-ichi Oshikiri 《manuscripta mathematica》2001,104(4):527-531
In this paper, we extend a result by H. Takagi on the non-existence of mutually commuting and linearly independent Killing
vector fields on positively curved Riemannian manifolds. Further, a kind of “Compact Leaf Theorem” is proved for metric foliations
of closed manifolds with positive sectional curvature.
Received: 26 May 2000 / Revised version: 28 February 2001 相似文献
10.
Finding Einstein solvmanifolds by a variational method 总被引:2,自引:0,他引:2
Jorge Lauret 《Mathematische Zeitschrift》2002,241(1):83-99
We use a variational approach to prove that any nilpotent Lie algebra having a codimension-one abelian ideal, and anyone
of dimension , admits a rank-one solvable extension which can be endowed with an Einstein left-invariant riemannian metric. A curve of
-dimensional Einstein solvmanifolds is also given.
Received: 29 May 2001; in final form: 4 October 2001 / Published online: 4 April 2002 相似文献
11.
S.V. Bolotin P.H. Rabinowitz 《Calculus of Variations and Partial Differential Equations》1999,9(2):125-139
This paper gives an extension of earlier work of Morse and of Hedlund on minimal heteroclinic geodesics for to the case of provided that an additional geometrical condition is satisfied. It also gives lower bounds on the number of such geodesics. 相似文献
12.
Xianghong Gong 《Mathematische Annalen》2002,323(2):227-257
We show that reversible holomorphic mappings of have periodic points accumulating at an elliptic fixed point of general type. On the contrary, we also show the existence
of holomorphic symplectic mappings that have no periodic points of certain periods in a sequence of deleted balls about an
elliptic fixed point of general type. The radii of the balls are carefully chosen in terms of the periods, which allows us
to show the existence of holomorphic mappi
ngs of that are not reversible with respect to any involution with a holomorphic linear part, and that admit no invariant totally real and real surfaces.
Received: 5 December 2000 / Published online: 4 April 2002 相似文献
13.
We show that a small neighborhood of a closed symplectic
submanifold in a geometrically bounded aspherical symplectic manifold has
non-vanishing symplectic homology. As a consequence, we establish the existence
of contractible closed characteristics on any thickening of the boundary
of the neighborhood. When applied to twisted geodesic flows on compact
symplectically aspherical manifolds, this implies
the existence of contractible periodic orbits for a dense set of
low energy values. 相似文献
14.
Konstantin Athanassopoulos 《manuscripta mathematica》1998,97(1):37-44
We construct examples of volume preserving non-singular C
1 vector fields on closed orientable 3-manifolds, which have cyclic winding numbers groups with respect to the preserved volume
element, but have no periodic orbits.
Received: 17 January 1998 / Revised version: 31 March 1998 相似文献
15.
Vladimir S. Matveev 《manuscripta mathematica》2001,105(3):343-352
Three-dimensional closed hyperbolic manifolds are geodesically rigid: if two metrics have the same geodesics then they are
homothetic.
Received: 16 March 2001 相似文献
16.
Antonio J. Ureña 《Archiv der Mathematik》2008,91(1):63-75
We consider the periodic action functional associated to some Lagrangian verifying the Legendre convexity condition and show
that all minimizers are unstable.
Supported by D.G.I. MTM2005-03483, Ministerio de Educación y Ciencia, Spain. 相似文献
17.
We prove a new lower bound for the first eigenvalue of the Dirac operator on a compact Riemannian spin manifold by refined
Weitzenb?ck techniques. It applies to manifolds with harmonic curvature tensor and depends on the Ricci tensor. Examples show
how it behaves compared to other known bounds.
Received: 20 April 2001 / Published online: 5 September 2002 相似文献
18.
Klaudiusz Wójcik 《Monatshefte für Mathematik》2002,135(3):245-252
We prove a sufficient condition for the existence of 2
n
(geometrically distinct) solutions of the two point boundary value problem
where .
Received 30 March 2001; in revised form 26 November 2001 相似文献
19.
Crossing estimates for symmetric Markov processes 总被引:2,自引:0,他引:2
A crossing estimate is established for symmetric Markov processes on general state spaces.
Received: 20 May 1999 / Revised version: 30 August 2000 / Published online: 9 March 2001 相似文献
20.
We study the geometric properties of the base manifold for the unit tangent bundle satisfying the η-Einstein condition with
the canonical contact metric structure. One of the main theorems is that the unit tangent bundle of 4-dimensional Einstein
manifold, equipped with the canonical contact metric structure, is η-Einstein manifold if and only if the base manifold is
the space of constant sectional curvature 1 or 2.
Authors’ addresses: Y. D. Chai, S. H. Chun, J. H. Park, Department of Mathematics, Sungkyunkwan University, Suwon 440-746,
Korea; K. Sekigawa, Department of Mathematics, Faculty of Science, Niigata University, Niigata, 950-2181, Japan 相似文献