Related papers: Spinor and Twistor Geometry in Einstein Gravity an…
We summarize some our recent results on encoding exact solutions of field equations in Einstein and modified gravity theories into solitonic hierarchies derived for nonholonomic curve flows with associated bi-Hamilton structure. We argue…
We discuss some of the issues to be addressed in arriving at a definitive noncommutative Riemannian geometry that generalises conventional geometry both to the quantum domain and to the discrete domain. This also provides an introduction to…
According to one of many equivalent definitions of twistors a (null) twistor is a null geodesic in Minkowski spacetime. Null geodesics can intersect at points (events). The idea of Penrose was to think of a spacetime point as a derived…
We study stress tensor correlation functions in four-dimensional conformal field theories with large $N$ and a sparse spectrum. Theories in this class are expected to have local holographic duals, so effective field theory in anti-de Sitter…
We consider models of accelerating Universe elaborated for Finsler like gravity theories constructed on tangent bundles to Lorentz manifolds. In the osculating approximation, certain locally anisotropic configurations are similar to those…
We study a deformation of infinitesimal diffeomorphisms of a smooth manifold. The deformation is based on a general twist. This leads to a differential geometry on a noncommutative algebra of functions whose product is a star-product. The…
This PhD dissertation covers a range of topics in Finsler geometry and Finsler gravity, most notably: (i) the characterization of Berwald spaces, (ii) pseudo-Riemann (non-)metrizability of Berwald spaces, (iii) $(\alpha,\beta)$-metrics,…
This is a doctoral thesis on the application of techniques originally developed in the programme of characterisation of supersymmetric solutions to Supergravity theories, to finding alternative backgrounds. We start by discussing the…
A consistent theory of quantum gravity (QG) at Planck scale almost sure contains manifestations of Lorentz local symmetry violations (LV) which may be detected at observable scales. This can be effectively described and classified by models…
This paper is the first in a series of paper where we describe the differential operators on general nonlinear metric measure spaces, namely, the Finsler spaces. We try to propose a general method for gradient estimates of the positive…
A common feature of all Quantum Gravity (QG) phenomenology approaches is to consider a modification of the mass shell condition of the relativistic particle to take into account quantum gravitational effects. The framework for such…
Lagrange geometry is the geometry of the tensor field defined by the fiberwise Hessian of a non degenerate Lagrangian function on the total space of a tangent bundle. Finsler geometry is the geometrically most interesting case of Lagrange…
In this paper, nonholonomic gerbes will be naturally derived for manifolds and vector bundle spaces provided with nonintegrable distributions (in brief, nonholonomic spaces). An important example of such gerbes is related to distributions…
The twistor method is applied for obtaining examples of generalized Kaehler structures which are not yielded by Kaehler structures.
The general relativity theory is redefined equivalently in almost Kahler variables: symplectic form and canonical symplectic connection (distorted from the Levi-Civita connection by a tensor constructed only from metric coefficients and…
Radu Miron's approach to modelling of generalized Lagrange, Finsler and Kaluza-Klein spaces on vector (super) bundles provided with compatible nonlinear and distinguished connections and metric structures is discussed in connection with the…
The Einstein equations (EE) are certain conditions on the Riemann tensor on the real Minkowski space M. In the twistor picture, after complexification and compactification M becomes the Grassmannian $Gr_{2}^{4}$ of 2-dimensional subspaces…
We discuss a generalisation of the Snyder model that includes all the possible deformations of the Heisenberg algebra compatible with Lorentz invariance, in terms of realisations of the noncommutative geometry. The corresponding deformed…
The article consists of the Russian and English variants of Ph.D. Thesis in which the answers is given on the following questions: 1. how to construct the spinor formalism for n=6; 2. how to construct the spinor formalism for n=8; 3. how to…
We propose the definition of (twisted) generalized hyperkaehler geometry and its relation to supersymmetric non-linear sigma models. We also construct the corresponding twistor space.