Related papers: Projective symplectic geometry on regular subspace…

A Riemannian metric on a manifold M induces a family of Riemannian metrics on the loop space LM depending on a Sobolev space parameter s. We compute the connection forms of these metrics and the higher symbols of their curvature forms,…

We consider an involutive automorphism of the conformal algebra and the resulting symmetric space. We display a new action of the conformal group which gives rise to this space. The space has an intrinsic symplectic structure, a…

We give an elementary construction of symplectic connections through reduction. This provides an elegant description of a class of symmetric spaces and gives examples of symplectic connections with Ricci type curvature, which are not…

In this paper we study coisotropic reduction in multisymplectic geometry. On the one hand, we give an interpretation of Hamiltonian multivector fields as Lagrangian submanifolds and prove that $k$-coisotropic submanifolds induce a Lie…

We explicitly describe the length minimizing geodesics for a sub-Riemannian structure of the elliptic type defined on $SL(2, \mathbb{R})$. Our method uses a symmetry reduction which translates the problem into a Riemannian problem on a two…

A symplectic structure on the space of nondegenerate and nonparametrized curves in a locally affine manifold is defined. We also consider several interesting spaces of nondegenerate projective curves endowed with Poisson structures. This…

We present a new approach for constructing covariant symplectic structures for geometrical theories, based on the concept of adjoint operators. Such geometric structures emerge by direct exterior derivation of underlying symplectic…

Projective connections arise from equivalence classes of affine connections under the reparametrization of geodesics. They may also be viewed as quotient systems of the classical geodesic equation. After studying the link between integrals…

We survey the progress on the study of symplectic geometry past five decades. The survey focuses on the convexity properties of a moment map, the classification of symplectic actions, the symplectic embedding problems, and the theory of…

Let $X$ be a union of a sequence of symplectic manifolds of increasing dimension and let $M$ be a manifold with a closed $2$-form $\omega$. We use Tischler's elementary method for constructing symplectic embeddings in complex projective…

We describe conditions under which a spacetime connection and a scaled Lorentzian metric define natural symplectic and Poisson structures on the tangent bundle of the Einstein spacetime.

We investigate the rudiments of Riemannian geometry on orbit spaces $M/G$ for isometric proper actions of Lie groups on Riemannian manifolds. Minimal geodesic arcs are length minimising curves in the metric space $M/G$ and they can hit…

Grafting is a surgery on Riemann surfaces introduced by Thurston which connects hyperbolic geometry and the theory of projective structures on surfaces. We will discuss the space of projective structures in terms of the Thurston's geometric…

We study the projective geometry of homogeneous varieties $X= G/P\subset P(V)$, where $G$ is a complex simple Lie group, $P$ is a maximal parabolic subgroup and $V$ is the minimal $G$-module associated to $P$. Our study began with the…

We provide an axiomatic approach to the theory of local tangent cones of regular sub-Riemannian manifolds and the differentiability of mappings between such spaces. This axiomatic approach relies on a notion of a dilation structure which is…

A family of naturally reductive pseudo-Riemannian spaces is constructed out of the representations of Lie algebras with ad-invariant metrics. We exhibit peculiar examples, study their geometry and characterize the corresponding naturally…

The geometry of generative models serves as the basis for interpolation, model inspection, and more. Unfortunately, most generative models lack a principal notion of geometry without restrictive assumptions on either the model or the data…

Given a Schubert class on $Gr(k,V)$ where $V$ is a symplectic vector space of dimension $2n$, we consider its restriction to the symplectic Grassmannian $SpGr(k,V)$ of isotropic subspaces. Pragacz gave tableau formulae for positively…

We show that the isomorphism between the moduli space of certain parabolic Higgs bundles over an elliptic curve and the Hilbert scheme of n points of the cotangent bundle of the elliptic curve is a symplectomorphism with respect to their…

We present a unified method of construction of surfaces associated with Grassmannian sigma models, expressed in terms of an orthogonal projector. This description leads to compact formulae for structural equations of two-dimensional…