Related papers: Geometric Poisson brackets on Grassmannians and co…

In this paper we use the relationship between conformal metrics on the sphere and horospherically convex hypersurfaces in the hyperbolic space for giving sufficient conditions on a conformal metric to be radial under some constrain on the…

This Thesis concerns a thin fluid shell embedded in its own gravitational field. The starting point is a work of Hajicek and Kijowski, where the hamiltonian formalism for shell(s) (with no symmetry) in Einstein gravity is developed. An open…

The classification of isoparametric hypersurfaces in spheres with four or six different principal curvatures is still not complete. In this paper we develop a structural approach that may be helpful for a classification. Instead of working…

This note describes a local Poisson structure (up to homotopy) associated to corners in four-dimensional gravity in the coframe (Palatini--Cartan) formalism. This is achieved through the use of the BFV formalism. The corner structure…

We connect two a priori unrelated topics, theory of geodesically equivalent metrics in differential geometry, and theory of compatible infinite dimensional Poisson brackets of hydrodynamic type in mathematical physics. Namely, we prove that…

Group lattices (Cayley digraphs) of a discrete group are in natural correspondence with differential calculi on the group. On such a differential calculus geometric structures can be introduced following general recipes of noncommutative…

It is shown that the new formula for the field theory Poisson brackets arise naturally in the extension of the formal variational calculus incorporating divergences. The linear spaces of local functionals, evolutionary vector fields,…

We show that if a generator of a differential Gerstenhaber algebra satisfies certain Cartan-type identities, then the corresponding Lie bracket is formal. Geometric examples include the shifted de Rham complex of a Poisson manifold and the…

We present some basic results on a natural Poisson structure on any compact symmetric space. The symplectic leaves of this structure are related to the orbits of the corresponding real semisimple group on the complex flag manifold.

For a class of Riemannian manifolds that include products of arbitrary compact manifolds with manifolds of nonpositive sectional curvature on the one hand, or with certain positive-curvature examples such as spheres of dimension at least 3…

Let G be a Lie group and g its Lie algebra. We develop a theory of quasi Poisson structures relative to a not necessarily non-degenerate Ad-invariant symmetric 2-tensor in the tensor square of g and one of general not necessarily…

Dilaton gravities in two dimensions can be formulated as particular Poisson sigma models. Target space diffeomorphisms map different models to each other and establish a one-to-one correspondence between their classical solutions. We obtain…

In recent years, a close connection between supergravity, string effective actions and generalized geometry has been discovered that typically involves a doubling of geometric structures. We investigate this relation from the point of view…

We undertake a detailed study of the geometry of Bottacin's Poisson structures on Hilbert schemes of points in Poisson surfaces, i.e. smooth complex surfaces equipped with an effective anticanonical divisor. We focus on three themes that,…

We study the moduli of G-local systems on smooth but not necessarily proper complex algebraic varieties. We show that, when suitably considered as derived algebraic stacks, they carry natural Poisson structures, generalizing the well known…

We present some new Poisson bivectors that are invariants by the flow of the nonholonomic Suslov problem. Two rank four invariant Poisson bivectors have globally defined Casimir functions and, therefore, define cubic Poisson brackets on the…

We show that the mean-field time dependent equations in the Phi^4 theory can be put into a classical non-canonical hamiltonian framework with a Poisson structure which is a generalization of the standard Poisson bracket. The Heisenberg…

We present a geometric construction of irreversible dynamics on Poisson manifolds that satisfies the axioms of metriplectic mechanics and the GENERIC framework. Our approach relies solely on the underlying Poisson structure and its…

We introduce a natural symplectic structure on the moduli space of quadratic differentials with simple zeros and describe its Darboux coordinate systems in terms of so-called homological coordinates. We then show that this structure…

We prove that, for 3 < m < n-1, the Grassmannian of m-dimensional subspaces of the space of skew-symmetric forms over a vector space of dimension n is birational to the Hilbert scheme of the degeneracy loci of m global sections of Omega(2),…