相关论文: On the complex structure of symplectic quotients

Suppose that a Lie group $G$ acts properly on a configuration manifold $Q$. We study the symplectic quotient of $T^*Q$ with respect to the cotangent lifted $G$-action at an arbitrary coadjoint orbit level $\mathcal{O}$. In particular, if…

We consider invariant symplectic connections $\nabla$ on homogeneous symplectic manifolds $(M,\omega)$ with curvature of Ricci type. Such connections are solutions of a variational problem studied by Bourgeois and Cahen, and provide an…

The (local) invariant symplectic action functional $\A$ is associated to a Hamiltonian action of a compact connected Lie group $\G$ on a symplectic manifold $(M,\omega)$, endowed with a $\G$-invariant Riemannian metric $<\cdot,\cdot>_M$. It…

We study complex Lagrangian submanifolds of a compact hyper-K\"ahler manifold and prove two results: (a) that an involution of a hyper-K\"ahler manifold which is antiholomorphic with respect to one complex structure and which acts…

Hamiltonian structures for spatially compact locally homogeneous vacuum universes are investigated, provided that the set of dynamical variables contains the \Teich parameters, parameterizing the purely global geometry. One of the key…

We use local symplectic Lie groupoids to construct Poisson integrators for generic Poisson structures. More precisely, recursively obtained solutions of a Hamilton-Jacobi-like equation are interpreted as Lagrangian bisections in a…

We study quadratic Lie algebras over a field K of null characteristic which admit, at the same time, a symplectic structure. We see that if K is algebraically closed every such Lie algebra may be constructed as the T*-extension of a…

We discuss symplectic manifolds where, locally, the structure is that encountered in Lagrangian dynamics. Exemples and characteristic properties are given. Then, we refer to the computation of the Maslov classes of a Lagrangian submanifold.…

We introduce a new class of Poisson structures on a Riemannian manifold. A Poisson structure in this class will be called a Killing-Poisson structure. The class of Killing-Poisson structures contains the class of symplectic structures, the…

Using methods from symplectic topology, we prove existence of invariant variational measures associated to the flow $\phi_H$ of a Hamiltonian $H\in C^{\infty}(M)$ on a symplectic manifold $(M,\omega)$. These measures coincide with Mather…

In this paper we study an integral invariant which obstructs the existence on a compact complex manifold of a volume form with the determinant of its Ricci form proportional to itself, in particular obstructs the existence of a…

In this paper we show that the Hamiltonian Monte Carlo method for compact Lie groups constructed in \cite{kennedy88b} using a symplectic structure can be recovered from canonical geometric mechanics with a bi-invariant metric. Hence we…

Let $(M,J)$ be a $n$-dimensional complex manifold: a $p$-K\"ahler structure (resp. $p$-symplectic structure) on $M$ is a real, closed $(p,p)$-transverse form $\Omega$ (resp. real, closed $2p$-form whose $(p,p)$-component is transverse). We…

A generalized complex manifold is locally gauge-equivalent to the product of a holomorphic Poisson manifold with a real symplectic manifold, but in possibly many different ways. In this paper we show that the isomorphism class of the…

The purpose of this article is to characterize symplectic and Hamiltonian circle actions on symplectic manifolds in terms of symplectic embeddings of Riemann surfaces. More precisely, we will show that (1) if $(M,\omega)$ admits a…

In this note we prove the following theorem: Let $G$ be a compact Lie group acting on a compact symplectic manifold $M$ in a Hamiltonian fashion. If $L$ is an $l$-dimensional closed invariant submanifold of $M$, on which the $G$-action is…

Multi-symplectic integrators are typically regarded as a discretization of the Hamiltonian partial differential equations. This is due to the fact that, for generic finite-dimensional Hamiltonian systems, there exists only one independent…

We prove that under certain conditions, the quantum cohomology of a positively monotone compact symplectic manifold is a deformation of the symplectic cohomology of the complement of a simple crossings symplectic divisor. We also prove…

We introduce scattering-symplectic manifolds, manifolds with a type of minimally degenerate Poisson structure that is not too restrictive so as to have a large class of examples, yet restrictive enough for standard Poisson invariants to be…

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…