Related papers: Hofer's metric in compact Lie groups

Following a question of F. Le Roux, we consider a system of invariants $l_A : H_1(M; \mathbb{Z})\to\mathbb{R}$ of a symplectic surface $M$. These invariants compute the minimal Hofer energy needed to translate a disk of area $A$ along a…

We introduce a notion of scalar curvature of a twisted generalized Kahler manifold in terms of pure spinors formalism. A moment map framework with a modified action of generalized Hamiltonians on an arbitrary compact generalized Kahler…

In this paper, we investigate the topology of a class of non-K\"ahler compact complex manifolds generalizing that of Hopf and Calabi-Eckmann manifolds. These manifolds are diffeomorphic to special systems of real quadrics in $\Bbb C^n$…

Let G be a complex reductive Lie group acting on a compact K\"ahler manifold X and assume that the action of a maximal compact subgroup K of G is Hamiltonian. For each extreme point of the convex hull of the momentum map image, there is an…

On a compact complex manifold $(M, J)$ endowed with a holomorphic Poisson tensor $\pi_J$ and a deRham class $\alpha\in H^2(M, \mathbb R)$, we study the space of generalized K\"ahler (GK) structures defined by a symplectic form $F\in \alpha$…

We construct completely integrable systems on the dual of the Lie algebra of any compact Lie group $K$ with respect to the standard Lie-Poisson structure. These systems generalize key properties of Gelfand-Zeitlin systems: A) the pullback…

We define the group of almost periodic diffeomorphisms on $\mathbb{R}^n$ and on an arbitrary Lie group. We then study the properties of its Riemannian and Lie group exponential maps and provide applications to fluid equations. In…

We investigate homogeneous geodesics in a class of homogeneous spaces called $M$-spaces, which are defined as follows. Let $G/K$ be a generalized flag manifold with $K=C(S)=S\times K_1$, where $S$ is a torus in a compact simple Lie group…

In this paper, we introduce the metric operator for a compact homogeneous Finsler space, and use it to investigate the geodesic orbit property. We define the notion of standard homogeneous $(\alpha_1,\cdots,\alpha_s)$-metric which…

Mapping class groups of Haken 3-manifolds enjoy many of the homological finiteness properties of mapping class groups of 2-manifolds of finite type. For example, H(M) has a torsionfree subgroup of finite index, which is geometrically finite…

I examine the Generalized K$\ddot{a}$hler geometry of classical $N=(2,2)$ superconformal WZW model on a compact group and relate the right-moving and left-moving Kac-Moody superalgebra currents to the Generalized K$\ddot{a}$hler geometry…

The main focus of the paper is the investigation of moduli space of left invariant pseudoRiemannian metrics on the cotangent bundle of Heisenberg group. Consideration of orbits of the automorphism group naturally acting on the space of the…

Associated to any manifold equipped with a closed form of degree >1 is an `L-infinity algebra of observables' which acts as a higher/homotopy analog of the Poisson algebra of functions on a symplectic manifold. In order to study Lie group…

We consider the Lie group of smooth diffeomorphisms Diff$(M)$ of a simple polytope $M$ in the euclidean space. Simple polytopes are special cases of manifolds with corners. The geometric setting allows to study in particular, the subgroup…

Let G be a regular Lie group which is a directed union of regular Lie groups G_i (all modelled on possibly infinite-dimensional, locally convex spaces). We show that G is the direct limit of the G_i as a regular Lie group whenever G admits…

We show that commutators of Hamiltonian diffeomorphisms may have arbitrarily large Hofer norm. The proposed technique is applicable to positive genus surfaces and their products. This gives partial answer to a question by McDuff and…

We study cohomogeneity one Riemannian manifolds and we establish some simple criterium to test when a singular orbit is totally geodesic. As an application, we classify compact, positively curved Riemannian manifolds which are acted on…

We study the role that Hamiltonian and symplectic diffeomorphisms play in the deformation problem of coisotropic submanifolds. We prove that the action by Hamiltonian diffeomorphisms corresponds to the gauge-action of the $L_\infty$-algebra…

Let us call pseudo-homothetic group the non-unimodular 3-dimensional Lie group that is the semi-direct product of $\mathbb{R}$ acting non-semisimply on $\mathbb{R}^2$. In this article, we solve the geodesic completeness problem on this Lie…

We investigate the geodesic orbit property of pseudo-Riemannian nilmanifolds, specifically those known in the literature as pseudo $H$-type Lie groups -- i.e., 2-step nilpotent Lie groups of Heisenberg type equipped with a left invariant…