Einstein-Weyl geometry is a triple (D,g,w), where D symmetric connection, [g] conformal structure and w covector such that: (i) connection preserves the class [g], that is, Dg=wg; (ii) trace-free part of symmetrised Ricci tensor vanishes. Three-dimensional structures arise naturally on solutions second-order dispersionless integrable PDEs in 3D. In this context, coincides with characteristic th...

Abstract Recently, an action principle for the limit of Einstein-Gauss-Bonnet gravity has been proposed. It is a special scalar-tensor theory that belongs to family Horndeski gravity. also well defined $D\rightarrow3$?> and $D\rightarrow2$?> limits. In this work, we examine in three four dimensions Bondi-Sachs framework. both dimensions, find there no news function ass...

The well-known self-similar solution for the two-point correlation function of the density field is valid only in an Einstein – de Sitter universe. We attempt to extend the solution for non – Einstein – de Sitter universes. For this purpose we introduce an idea of quasi-self-similar evolution; this approach is based on the assumption that the evolution of the two-point correlation is a successi...

The role of space-time torsion in general relativity is reviewed in accordance with some recent results on the subject. It is shown that, according to the connection compatibility condition, the usual Riemannian volume element is not appropriate in the presence of torsion. A new volume element is proposed and used in the Lagrangian formulation for Einstein-Cartan theory of gravity. The dynamica...

We formulate an approach to the geometry of Riemann–Cartan spaces provided with nonholonomic distributions defined by generic off–diagonal and nonsymmetric metrics inducing effective nonlinear and affine connections. Such geometries can be modelled by moving nonholonomic frames on (pseudo) Riemannian manifolds and describe various types of nonholonomic Einstein, Eisenhart–Moffat and Finsler–Lag...

Many important features of a eld theory, e.g., conserved currents, symplectic structures, energy-momentumtensors, etc., arise as tensors locally constructed from the elds and their derivatives. Such tensors are naturally de ned as geometric objects on the jet space of solutions to the eld equations. Modern results from the calculus on jet bundles can be combined with a powerful spinor parametri...

N. Hitchin [H] proved that the Euler characteristic χ(E) and signature σ(E) of a compact orientable 4-dimensional Einstein manifold E satisfy the inequality |σ(E)| 6 2 3χ(E), the equality holding only if either E is flat or the universal covering X of E is a K3-surface and π1(E) = 1, Z/2, or Z/2× Z/2. In the latter cases, E is a K3-surface if π1 = 1, an Enriques surface if π1 = Z/2, or the quot...