共查询到20条相似文献,搜索用时 15 毫秒
1.
On the path space over a compact Riemannian manifold, the global existence and the global uniqueness of the quasi-invariant geodesic flows with respect to a negative Markov connection are obtained in this paper. The results answer affirmatively a left problem of Li. 相似文献
2.
Božidar Jovanović 《Regular and Chaotic Dynamics》2011,16(5):504-513
We prove the integrability of geodesic flows on the Riemannian g.o. spaces of compact Lie groups, as well as on a related
class of Riemannian homogeneous spaces having an additional principal bundle structure. 相似文献
3.
向开南 《中国科学A辑(英文版)》2002,45(4):409-419
Some interesting quasi-invariant transformations on the path space over a Riemannian manifold are investigated. The results
improve some previous ones.
An erratum to this article is available at . 相似文献
4.
Jinghai Shao 《Stochastic Processes and their Applications》2019,129(1):153-173
In this work we prove the existence and uniqueness of the optimal transport map for -Wasserstein distance with , and particularly present an explicit expression of the optimal transport map for the case . As an application, we show the existence of geodesics connecting probability measures satisfying suitable condition on path groups and loop groups. 相似文献
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6.
Following on from our previous study of the geodesic flow on three dimensional ellipsoid with equal middle semi-axes, here
we study the remaining cases: Ellipsoids with two sets of equal semi-axes with SO(2) × SO(2) symmetry, ellipsoids with equal larger or smaller semiaxes with SO(2) symmetry, and ellipsoids with three semi-axes coinciding with SO(3) symmetry. All of these cases are Liouville-integrable, and reduction of the symmetry leads to singular reduced systems
on lower-dimensional ellipsoids. The critical values of the energy-momentum maps and their singular fibers are completely
classified. In the cases with SO(2) symmetry there are corank 1 degenerate critical points; all other critical points are non-degenreate. We show that in
the case with SO(2) × SO(2) symmetry three global action variables exist and the image of the energy surface under the energy-momentum map is a convex
polyhedron. The case with SO(3) symmetry is non-commutatively integrable, and we show that the fibers over regular points of the energy-casimir map are
T
2 bundles over S
2.
相似文献
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8.
In this paper, we generalize geodesic $E$-convex function and define geodesic $\gamma$-pre-$E$-convex and geodesic $\gamma$-$E$-convex functions on Riemannian manifolds. The sufficient condition of equivalence class of geodesic $\gamma$-pre-$E$-convexity and geodesic $\gamma$-$E$-convexity for differentiable function on Riemannian manifolds is studied. We discuss the sufficient condition for $E$-epigraph to be geodesic $E$-convex set. At the end, we establish some optimality results with the aid of geodesic $\gamma$-pre-$E$-convex and geodesic $\gamma$-$E$-convex functions and discuss the mean value inequality for geodesic $\gamma$-pre-$E$-convex function. 相似文献
9.
LI Zhong LMAM & School of Mathematical Sciences Peking University Beijing China 《中国科学A辑(英文版)》2005,(8)
Let T(S) be the Teichmuller space of a Riemann surface S. By definition, a geodesic disc in T(S) is the image of an isometric embedding of the Poincare disc into T(S). It is shown in this paper that for any non-Strebel point τ∈T(S), there are infinitely many aeodesic discs containina [0] and τ. 相似文献
10.
For two vertices u and v of a graph G, the closed interval I[u, v] consists of u, v, and all vertices lying in some u–v geodesic of G, while for S V(G), the set I[S] is the union of all sets I[u, v] for u, v S. A set S of vertices of G for which I[S] = V(G) is a geodetic set for G, and the minimum cardinality of a geodetic set is the geodetic number g(G). A vertex v in G is an extreme vertex if the subgraph induced by its neighborhood is complete. The number of extreme vertices in G is its extreme order ex(G). A graph G is an extreme geodesic graph if g(G) = ex(G), that is, if every vertex lies on a u–v geodesic for some pair u, v of extreme vertices. It is shown that every pair a, b of integers with 0 a b is realizable as the extreme order and geodetic number, respectively, of some graph. For positive integers r, d, and k 2, it is shown that there exists an extreme geodesic graph G of radius r, diameter d, and geodetic number k. Also, for integers n, d, and k with 2 d > n, 2 k > n, and n – d – k + 1 0, there exists a connected extreme geodesic graph G of order n, diameter d, and geodetic number k. We show that every graph of order n with geodetic number n – 1 is an extreme geodesic graph. On the other hand, for every pair k, n of integers with 2 k n – 2, there exists a connected graph of order n with geodetic number k that is not an extreme geodesic graph. 相似文献
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12.
Pedro Ontaneda 《Geometriae Dedicata》2004,104(1):25-35
We study the following question: does a compact nonpositively curved space have a totally geodesic core? 相似文献
13.
约束力学系统的联络及其运动方程的测地性质 总被引:2,自引:0,他引:2
用现代整体微分几何方法研究非定常约束力学系统运动方程的测地性质,得到非定常力学系统的动力学流关于1_射丛上的联络具有测地性质的充分必要条件·非定常情形下的动力学流关于无挠率的联络总具有测地性质,因此任何非定常约束力学系统在外力作用下的运动总可以表示为关于1_射丛上无挠率的动力学联络的测地运动,这与定常力学的情形有所区别· 相似文献
14.
Isaac Vikram Chenchiah Marc Oliver Rieger Johannes Zimmer 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(11):5820-5834
This article is concerned with gradient flows in asymmetric metric spaces, that is, spaces with a topology induced by an asymmetric metric. Such an asymmetry appears naturally in many applications, e.g., in mathematical models for materials with hysteresis. A framework of asymmetric gradient flows is established under the assumption that the metric is weakly lower-semicontinuous in the second argument (and not necessarily on the first), and an existence theorem for gradient flows defined on an asymmetric metric space is given. 相似文献
15.
José Barbosa Gomes Rafael O. Ruggiero 《Proceedings of the American Mathematical Society》2007,135(2):507-515
Let be a closed orientable surface. Assume that there exists a codimension one foliation of class in the unit tangent bundle of , whose leaves are invariant under the geodesic flow of . Then, the curvature of is a nonpositive constant.
16.
T. Rapcsák 《Journal of Optimization Theory and Applications》1991,69(1):169-183
The properties of geodesic convex functions defined on a connected RiemannianC
2
k-manifold are investigated in order to extend some results of convex optimization problems to nonlinear ones, whose feasible region is given by equalities and by inequalities and is a subset of a nonlinear space.This research was supported in part by the Hungarian National Research Foundation, Grant No. OTKA-1044. 相似文献
17.
Kenro Furutani 《Annals of Global Analysis and Geometry》2002,22(1):1-27
We study a problem of the geometric quantization for the quaternionprojective space. First we explain a Kähler structure on the punctured cotangent bundleof the quaternion projective space, whose Kähler form coincides withthe natural symplectic form on the cotangent bundle and show thatthe canonical line bundle of this complex structure is holomorphicallytrivial by explicitly constructing a nowhere vanishing holomorphicglobal section. Then we construct a Hilbert space consisting of acertain class of holomorphic functions on the punctured cotangentbundle by the method ofpairing polarization and incidentally we construct an operatorfrom this Hilbert space to the L
2 space of the quaternionprojective space. Also we construct a similar operator between thesetwo Hilbert spaces through the Hopf fiberation.We prove that these operators quantizethe geodesic flow of the quaternion projective space tothe one parameter group of the unitary Fourier integral operatorsgenerated by the square root of the Laplacian plus suitable constant.Finally we remark that the Hilbert space above has the reproducing kernel. 相似文献
18.
Sally Kuhlmann 《Geometriae Dedicata》2008,131(1):181-211
We consider the existence of simple closed geodesics or “geodesic knots” in finite volume orientable hyperbolic 3-manifolds.
Every such manifold contains at least one geodesic knot by results of Adams, Hass and Scott in (Adams et al. Bull. London
Math. Soc. 31: 81–86, 1999). In (Kuhlmann Algebr. Geom. Topol. 6: 2151–2162, 2006) we showed that every cusped orientable hyperbolic 3-manifold in fact contains infinitely many geodesic
knots. In this paper we consider the closed manifold case, and show that if a closed orientable hyperbolic 3-manifold satisfies
certain geometric and arithmetic conditions, then it contains infinitely many geodesic knots. The conditions on the manifold
can be checked computationally, and have been verified for many manifolds in the Hodgson-Weeks census of closed hyperbolic
3-manifolds. Our proof is constructive, and the infinite family of geodesic knots spiral around a short simple closed geodesic
in the manifold.
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19.
We prove that a Riemannian manifold is harmonic if and only if there exists a divergence-preserving geodesic transformation
with respect to each point which is not volume-preserving. 相似文献
20.
We prove commutative integrability of the Hamilton system on the tangent bundle of the complex projective space whose Hamiltonian coincides with the Hamiltonian of the geodesic flow and the Poisson bracket deforms due to addition of the Fubini–Study form to the standard symplectic form. 相似文献