共查询到20条相似文献,搜索用时 421 毫秒
1.
We calculate the Hörmander index in the finite-dimensional case. Then we use the result to give some iteration inequalities, and prove almost existence of mean indices for given complete autonomous Hamiltonian system on compact symplectic manifold with symplectic trivial tangent bundle and given autonomous Hamiltonian system on regular compact energy hypersurface of symplectic manifold with symplectic trivial tangent bundle. 相似文献
2.
Daniel Guan 《Transactions of the American Mathematical Society》2005,357(8):3359-3373
In this note we give a structure theorem for a finite-dimensional subgroup of the automorphism group of a compact symplectic manifold. An application of this result is a simpler and more transparent proof of the classification of compact homogeneous spaces with invariant symplectic structures. We also give another proof of the classification from the general theory of compact homogeneous spaces which leads us to a splitting conjecture on compact homogeneous spaces with symplectic structures (which are not necessary invariant under the group action) that makes the classification of this kind of manifold possible.
3.
We consider compact symplectic manifolds acted on effectively by a compact connected Lie group K in a Hamiltonian fashion. We prove that the squared moment map ∥μ∥2 is constant if and only if K is semisimple and the manifold is K-equivariantly symplectomorphic to a product of a flag manifold and a compact symplectic manifold which is acted on trivially by K. In the almost-Kähler setting the symplectomorphism turns out to be an isometry. 相似文献
4.
Victor Guillemin Eva Miranda Ana Rita Pires 《Bulletin of the Brazilian Mathematical Society》2011,42(4):607-623
In this short note we give a complete characterization of a certain class of compact corank one Poisson manifolds, those equipped with a closed one-form defining the symplectic foliation and a closed two-form extending the symplectic form on each leaf. If such a manifold has a compact leaf, then all the leaves are compact, and furthermore the manifold is a mapping torus of a compact leaf. These manifolds and their regular Poisson structures admit an extension as the critical hypersurface of a b-Poisson manifold as we will see in [9]. 相似文献
5.
In this paper we generalize to coisotropic actions of compact Lie groups a theorem of Guillemin on deformations of Hamiltonian
structures on compact symplectic manifolds. We show how one can reconstruct from the moment polytope the symplectic form on
the manifold.
Received: 21 March 2006 相似文献
6.
Tedi Dr?ghici 《Differential Geometry and its Applications》2005,22(2):147-158
It is shown that the existence of an ω-compatible Einstein metric on a compact symplectic manifold (M,ω) imposes certain restrictions on the symplectic Chern numbers. Examples of symplectic manifolds which do not satisfy these restrictions are given. The results offer partial support to a conjecture of Goldberg. 相似文献
7.
Yves Benoist 《Geometriae Dedicata》2002,89(1):177-241
For any symplectic action of a compact connected group on a compact connected symplectic manifold, we show that the intersection
of the Weyl chamber with the image of the moment map is a closed convex polyhedron. This extends Atiyah–Guillemin–Sternberg–Kirwan's
convexity theorems to non-Hamiltonian actions. As a consequence, we describe those symplectic actions of a torus which are
coisotropic (or multiplicity free), i.e. which have at least one coisotropic orbit: they are the product of an Hamiltonian
coisotropic action by an anhamiltonian one. The Hamiltonian coisotropic actions have already been described by Delzant thanks
to the convex polyhedron. The anhamiltonian coisotropic actions are actions of a central torus on a symplectic nilmanifold.
This text is written as an introduction to the theory of symplectic actions of compact groups since complete proofs of the
preliminary classical results are given.
An erratum to this article is available at . 相似文献
8.
Using Donaldson's approximately holomorphic techniques, we construct symplectic hypersurfaces lying in the complement of
any given compact isotropic submanifold of a compact symplectic manifold. We discuss the connection with rational convexity
results in the K?hler case and various applications.
Received: 9 January 2001 / Published online: 19 October 2001 相似文献
9.
Andrea Giacobbe 《Geometriae Dedicata》2005,111(1):1-22
A famous theorem of Atiyah, Guillemin and Sternberg states that, given a Hamiltonian torus action, the image of the momentum map is a convex polytope. We prove that this result can be extended to the case in which the action is non-Hamiltonian. Our generalization of the theorem states that, given a symplectic torus action, the momentum map can be defined on an appropriate covering of the manifold and its image is the product of a convex polytope along a rational subspace times the orthogonal vector space. We also prove that this decomposition in direct product is stable under small equivariant perturbations of the symplectic structure; this, in particular, means that the property of being Hamiltonian is locally stable. The technique developed allows us to extend the result to any compact group action and also to deduce that any symplectic n-torus action, with fixed points, on a compact 2n-dimensional manifold, is Hamiltonian. 相似文献
10.
We develop a bundle picture for singular symplectic quotients of cotangent bundles acted upon by cotangent lifted actions for the case that the configuration manifold is of single orbit type. Furthermore, we give a formula for the reduced symplectic form in this setting. As an application of this bundle picture we consider Calogero–Moser systems with spin associated to polar representations of compact Lie groups. 相似文献
11.
Ioannis D. Platis 《Geometriae Dedicata》2001,87(1-3):17-34
We study the complex symplectic geometry of the space QF(S) of quasi-Fuchsian structures of a compact orientable surface S of genus g > 1. We prove that QF(S) is a complex symplectic manifold. The complex symplectic structure is the complexification of the Weil–Petersson symplectic structure of Teichmüller space and is described in terms which look natural from the point of view of hyperbolic geometry. 相似文献
12.
A holomorphic Lagrangian fibration on a holomorphically symplectic manifold is a holomorphic map with Lagrangian fibers. It is known (due to Huybrechts) that a given compact manifold admits only finitely many holomorphic symplectic structures, up to deformation. We prove that a given compact, simple hyperkähler manifold with b2?7 admits only finitely many deformation types of holomorphic Lagrangian fibrations. We also prove that all known hyperkähler manifolds are never Kobayashi hyperbolic. 相似文献
13.
《中国科学 数学(英文版)》2017,(6)
We prove an estimate for Donaldson's Q-operator on a prequantized compact symplectic manifold.This estimate is an ingredient in the recent result of Keller and Lejmi(2017) about a symplectic generalization of Donaldson's lower bound for the L~2-norm of the Hermitian scalar curvature. 相似文献
14.
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
15.
We study the orbit structure and the geometric quantization of a pair of mutually commuting hamiltonian actions on a symplectic manifold. If the pair of actions fulfils a symplectic Howe condition, we show that there is a canonical correspondence between the orbit spaces of the respective moment images. Furthermore, we show that reduced spaces with respect to the action of one group are symplectomorphic to coadjoint orbits of the other group. In the Kähler case we show that the linear representation of a pair of compact connected Lie groups on the geometric quantization of the manifold is then equipped with a representation-theoretic Howe duality. 相似文献
16.
17.
Christopher Allday Volker Hauschild Volker Puppe 《Transactions of the American Mathematical Society》2002,354(7):2971-2982
We prove that, under certain conditions, if a compact connected Lie group acts effectively on a closed manifold, then there is no fixed point. Because two of the main conditions are satisfied by any Hamiltonian action on a closed symplectic manifold, the theorem applies nicely to such actions. The method of proof, however, is cohomological; and so the result applies more generally.
18.
We construct examples of symplectic half-flat manifolds on compact quotients of solvable Lie groups. We prove that the Calabi-Yau
structures are not rigid in the class of symplectic half-flat structures. Moreover, we provide an example of a compact 6-dimensional
symplectic half-flat manifold whose real part of the complex volume form is d-exact. Finally we discuss the 4-dimensional case.
This work was supported by the Projects M.I.U.R. “Geometric Properties of Real and Complex Manifolds”, “Riemannian Metrics
and Differentiable Manifolds” and by G.N.S.A.G.A. of I.N.d.A.M. 相似文献
19.
We prove an estimate for Donaldson’s Q-operator on a prequantized compact symplectic manifold. This estimate is an ingredient in the recent result of Keller and Lejmi (2017) about a symplectic generalization of Donaldson’s lower bound for the L 2-norm of the Hermitian scalar curvature. 相似文献