相关论文: Isotropic embeddings of coadjoint orbits and magne…

Using a basic idea of Sullivan's rational homotopy theory, one can see a Lie groupoid as the fundamental groupoid of its Lie algebroid. This paper studies analogues of Lie algebroids with non-trivial higher homotopy. Using various homotopy…

This paper is a review of recent and classical results on integrable geodesic flows on Riemannian manifolds and topological obstructions to integrability. We also discuss some open problems.

In this paper, we introduce a geometric flow for Lagrangian submanifolds in a K\"ahler manifold that stays in its initial Hamiltonian isotopy class and is a gradient flow for volume. The stationary solutions are the Hamiltonian stationary…

We use cotangent bundles of spaces of smooth embeddings to construct symplectic dual pairs involving the group of volume preserving diffeomorphisms. Via symplectic reduction we obtain descriptions of coadjoint orbits of this group in terms…

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 $SO(2) \times SO(2)$ symmetry,…

Spherically symmetric solutions of the SU(N) Einstein-Yang-Mills-Higgs system are constructed using the harmonic map ansatz. The problem reduces to solving a set of ordinary differential equations for the appropriate profile functions. In…

We study the general geometrical structure of the coadjoint orbits of a semidirect product formed by a Lie group and a representation of this group on a vector space. The use of symplectic induction methods gives new insight into the…

The fact that the modular template coincides with the Lorenz template, discovered by Ghys, implies modular knots have very peculiar properties. We obtain a generalization of these results to other Hecke triangle groups. In this context, the…

This paper gives two results that show that the dynamics of a time-periodic Lagrangian system on a hyperbolic manifold are at least as complicated as the geodesic flow of a hyperbolic metric. Given a hyperbolic geodesic in the Poincar\'e…

Our main is to study periodic orbits of linear and invariant flows on a real, connected Lie group. Since each linear flow $\varphi_t$ has a derivation associated $\mathcal{D}$, we show that the existence of periodic orbits of $\varphi_t$ is…

The geometric quantization of the geodesic flow on a compact Riemannian manifold via the BKS "dragging projection" yields the Laplacian plus a scalar curvature term. To avoid convergence issues, the standard construction involves somewhat…

Let ${\bf H}_{\mathbb C}^n$ be the $n$-dimensional complex hyperbolic space and ${\rm SU}(n,1)$ be the (holomorphic) isometry group. An element $g$ in ${\rm SU}(n,1)$ is called loxodromic or hyperbolic if it has exactly two fixed points on…

Homogeneous compatible almost complex structures on symplectic manifolds are studied, focusing on those which are special, meaning that their Chern-Ricci form is a multiple of the symplectic form. Non Chern-Ricci flat ones are proven to be…

Brinkmann Lorentz manifolds are those admitting an isotropic parallel vector field. We prove geodesic completeness of the compact and also compactly homogeneous Brinkmann spaces. We also prove, partially, that their parallel vector field…

We prove complete integrability of the Manakov-type SO(n)-invariant geodesic flows on homogeneous spaces $SO(n)/SO(k_1)\times...\times SO(k_r)$, for any choice of $k_1,...,k_r$, $k_1+...+k_r\le n$. In particular, a new proof of the…

We characterize isometric actions on compact Kaehler manifolds admitting a Lagrangian orbit, describing under which condition the Lagrangian orbit is unique. We furthermore give the complete classification of simple groups acting on the…

In this paper we study rigidity aspects of Zoll magnetic systems on closed surfaces. We characterize magnetic systems on surfaces of positive genus given by constant curvature metrics and constant magnetic functions as the only magnetic…

The topology of the embedding of the coadjoint orbits of the unitary group U(H) of an in-finite dimensional complex Hilbert space H, as canonically determined subsets of the B-space T_s of symmetric trace class operators, is investigated.…

We construct Riemannian manifolds with completely integrable geodesic flows, in particular various nonhomogeneous examples. The methods employed are a modification of Thimm's method, Riemannian submersions and connected sums.

We study the dynamics of magnetic flows on Heisenberg groups. Let $H$ denote the three-dimensional simply connected Heisenberg Lie group endowed with a left-invariant Riemannian metric and an exact, left-invariant magnetic field. Let…