共查询到20条相似文献,搜索用时 15 毫秒
1.
Minoru Tanaka 《Geometriae Dedicata》1991,40(3):361-366
An isometry A on a Riemannian manifold M will be called of compact type if the subgroup generated by A is relatively compact in the isometry group of M. A geodesic : RM is called invariant under the isometry A if there exists a nonzero constant b such that A(t)=(t+b) for any real t. We prove that if A is an isometry of compact type on a connected Riemannian manifold, and if A has a nonclosed invariant geodesic, then A has uncountably many invariant geodesics. 相似文献
2.
Enrique Macias Virgós 《Annals of Global Analysis and Geometry》1993,11(1):35-40
We obtain several homotopy obstructions to the existence of non-closed connected Lie subgroupsH in a connected Lie groupG.First we show that the foliationF(G, H) onG determined byH is transversely complete [4]; moreover, forK the closure ofH inG, F(K, H) is an abelian Lie foliation [2].Then we prove that 1(K) and 1(H) have the same torsion subgroup,
n
(K)=
n
(H) for alln 2, and rank1(K) — rank1(H) > codimF(K, H). This implies, for instance, that a contractible (e.g. simply connected solvable) Lie subgroup of a compact Lie group must be abelian. Also, if rank1(G) 1 then any connected invariant Lie subgroup ofG is closed; this generalizes a well-known theorem of Mal'cev [3] for simply connected Lie groups.Finally, we show that the results of Van Est on (CA) Lie groups [6], [7] provide many interesting examples of such foliations. Actually, any Lie group with non-compact centre is the (dense) leaf of a foliation defined by a closed 1-form. Conversely, when the centre is compact, the latter is true only for (CA) Lie groups (e.g. nilpotent or semisimple). 相似文献
3.
P. G. Dixon 《Proceedings of the American Mathematical Society》2000,128(12):3647-3654
A major difficulty in Banach algebra theory is that sums of closed ideals need not be closed. We survey the known results and present examples showing that they are in most directions the best possible. We also give a new sufficient condition for closure in the uniform algebra setting.
4.
5.
Daniel Offin 《Transactions of the American Mathematical Society》2000,352(7):3323-3338
We apply the intersection theory for Lagrangian submanifolds to obtain a Sturm type comparison theorem for linearized Hamiltonian flows. Applications to the theory of geodesics are considered, including a sufficient condition that arclength minimizing closed geodesics, for an -dimensional Riemannian manifold, are hyperbolic under the geodesic flow. This partially answers a conjecture of G. D. Birkhoff.
6.
Let M be a manifold with linear connection . The space G(M) of all geodesics of M may be given a topological structure and may be realized as a quotient space of the reduced tangent bundle of M. The space G(M) is a T
1 space iff the image of each geodesic is a closed subset of M. It is Hausdorff iff each tangentially convergent sequence of geodesics converges in the Hausdorff limit sense to the limit geodesic. If M has no conjugate points and G(M) is Hausdorff, then M is geodesically connected.Supported in part by NSF grant DMS-8803511. 相似文献
7.
K. Guruprasad 《Topology》2006,45(3):611-641
In this paper, we try to generalize to the case of compact Riemannian orbifolds Q some classical results about the existence of closed geodesics of positive length on compact Riemannian manifolds M. We shall also consider the problem of the existence of infinitely many geometrically distinct closed geodesics.In the classical case the solution of those problems involve the consideration of the homotopy groups of M and the homology properties of the free loop space on M (Morse theory). Those notions have their analogue in the case of orbifolds. The main part of this paper will be to recall those notions and to show how the classical techniques can be adapted to the case of orbifolds. 相似文献
8.
C.A Botsaris 《Journal of Mathematical Analysis and Applications》1981,79(2):295-306
An arc method is presented for solving the equality constrained nonlinear programming problem. The curvilinear search path used at each iteration of the algorithm is a second-order approximation to the geodesic of the constraint surface which emanates from the current feasible point and has the same initial heading as the projected negative gradient at that point. When the constraints are linear, or when the step length is sufficiently small, the algorithm reduces to Rosen's Gradient Projection Method. 相似文献
9.
10.
Karlhofer Bastien Kędra Jarek Marcinkowski Michał Trost Alexander 《Geometriae Dedicata》2021,213(1):523-530
Geometriae Dedicata - We investigate the geometry of word metrics on fundamental groups of manifolds associated with the generating sets consisting of elements represented by closed geodesics. We... 相似文献
11.
If all prime closed geodesics on (Sn, F) with an irreversible Finsler metric F are irrationally elliptic, there exist either exactly 2 \(\left[ {\frac{{n + 1}}{2}} \right]\) or infinitely many distinct closed geodesics. As an application, we show the existence of three distinct closed geodesics on bumpy Finsler (S3, F) if any prime closed geodesic has non-zero Morse index. 相似文献
13.
14.
In pseudo-Riemannian geometry the spaces of space-like and time-like geodesics on a pseudo-Riemannian manifold have natural symplectic structures (just like in the Riemannian case), while the space of light-like geodesics has a natural contact structure. Furthermore, the space of all geodesics has a structure of a Jacobi manifold. We describe the geometry of these structures and their generalizations. We also introduce and study pseudo-Euclidean billiards, emphasizing their distinction from Euclidean ones. We present a pseudo-Euclidean version of the Clairaut theorem on geodesics on surfaces of revolution. We prove pseudo-Euclidean analogs of the Jacobi–Chasles theorems and show the integrability of the billiard in the ellipsoid and the geodesic flow on the ellipsoid in a pseudo-Euclidean space. 相似文献
15.
We characterize polyhedral surfaces admitting a simple dense geodesic ray and convex polyhedral surfaces with a simple geodesic ray. 相似文献
16.
Martingale optimal transport has attracted much attention due to its application in pricing and hedging in mathematical finance. The essential notion which makes martingale optimal transport different from optimal transport is peacock. A peacock is a sequence of measures which satisfies convex order property. In this paper we study peacock geodesics in Wasserstain space, and we hope this paper can provide some geometrical points of view to look at martingale optimal transport. 相似文献
17.
18.
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
19.
Mark Pollicott 《Israel Journal of Mathematics》1985,52(3):209-224
In this paper the distribution of closed geodesics on surfaces of constant negative curvature are studied from a dynamical
viewpoint. Asymptotic estimates are derived independently of the work of Selberg or Margulis, or the work of Bowen on Axiom
A flows. 相似文献
20.
《Nonlinear Analysis: Theory, Methods & Applications》2001,47(5):3005-3017