Related papers: Two constructions with parabolic geometries

We investigate geometric properties of homogeneous parabolic geometries with generalized symmetries. We show that they can be reduced to a simpler geometric structures and interpret them explicitly. For specific types of parabolic…

In this survey paper we give an overview over constructions of geometries associated to Jordan structures (algebras, triple systems and pairs), featuring analogs of these constructions with the Lie functor on the one hand and with the…

We study sets of solutions to equations over a free group, projections of such sets, and the structure of elementary sets defined over a free group. The structre theory we obtain enable us to answer some questions of A. Tarski's, and…

This paper contains a thorough introduction to the basic geometric properties of the manifold of Lagrangian subspaces of a linear symplectic space, known as the Lagrangian Grassmannian. It also reviews the important relationship between…

We investigate the geometric and topological structure of equidistant decompositions of Riemannian manifolds.

Path geometries provide a geometric encoding of systems of second order ODE, which serves as a model for the geometric theory of more general systems of ODE and for cone structures. They are an instance of the family of parabolic…

The relationship between spinors and Clifford (or geometric) algebra has long been studied, but little consistency may be found between the various approaches. However, when spinors are defined to be elements of the even subalgebra of some…

The aim of this paper is to present a short introduction to supergeometry on pure odd supermanifolds. (Pseudo)differential forms, Cartan calculus (DeRham differential, Lie derivative, "inner" product), metric, inner product, Killing's…

Following our approach to metric Lie algebras developed in math.DG/0312243 we propose a way of understanding pseudo-Riemannian symmetric spaces which are not semi-simple. We introduce cohomology sets (called quadratic cohomology) associated…

This note is the sequel of "Geometric structures as variational objects, I." It generalizes the main result and perspectives of that work to a class of geometric structures that includes integrable almost-complex structures.

These notes give an introduction to the equivalence problem of sub-Riemannian manifolds. We first introduce preliminaries in terms of connections, frame bundles and sub-Riemannian geometry. Then we arrive to the main aim of these notes,…

We compare and contrast two approaches to the structure theory for Lie pseudo-groups, the first due to Cartan, and the second due to the first two authors. We argue that the latter approach offers certain advantages from both a theoretical…

We construct an additive category where objects are embedded graphs in the 3-sphere and morphisms are geometric correspondences given by 3-manifolds realized in different ways as branched covers of the 3-sphere, up to branched cover…

There are studied in details 5-dimensional pseudo-Riemannian manifolds equipped with the structure analogous to the almost cosymplectic (almost coKaehler) structure. The curvature by assumption commutes with the structure affinor and all…

We review in a pedagogical manner some of the efforts aiming to extend the gauge/gravity correspondence to non-conformal supersymmetric gauge theories in four dimensions. After giving a general overview, we discuss in detail two specific…

We define and study an extended hyperbolic space which contains the hyperbolic space and de Sitter space as subspaces and which is obtained as an analytic continuation of the hyperbolic space. The construction of the extended space gives…

We introduce length dilatation structures on metric spaces, tempered dilatation structures and coherent projections and explore the relations between these objects and the Radon-Nikodym property and Gamma-convergence of length functionals.…

For Grassmann varieties, we explain how the duality between the Gelfand-Tsetlin polytopes and the Feigin-Fourier-Littelmann-Vinberg polytopes arises from different positive structures.

The paper is devoted to the study of geodesic orbit Riemannian spaces that could be characterize by the property that any geodesic is an orbit of a 1-parameter group of isometries. In particular, we discuss some important totally geodesic…

The purpose of this article is to analyze several Lie algebras associated to "orbit configuration spaces" obtained from a group G acting freely, and properly discontinuously on the upper 1/2-plane H^2. The Lie algebra obtained from the…