Related papers: Affine metrics and algebroid structures: Applicati…
In a class of generalized Einstein's gravity theories we derive the equations and general asymptotic solutions describing the evolution of the perturbed universe in unified forms. Our gravity theory considers general couplings between the…
We study algebraic and geometric properties of metric spaces endowed with dilatation structures, which are emergent during the passage through smaller and smaller scales. In the limit we obtain a generalization of metric affine geometry,…
We consider classical gauge theory with spontaneous symmetry breaking on a principal bundle $P\to X$ whose structure group $G$ is reducible to a closed subgroup $H$, and sections of the quotient bundle $P/H\to X$ are treated as classical…
Two new classes of metrizable vector bundles have been presented in the papers [1] and [4]. The Lie algebroid generalized tangent bundle of a dual vector bundle is presented. This Lie algebroid is a new example of metrizable vector bundle.…
A new formalism for spinors on curved spaces is developed in the framework of variational calculus on fibre bundles. The theory has the same structure of a gauge theory and describes the interaction between the gravitational field and…
An almost Einstein manifold satisfies equations which are a slight weakening of the Einstein equations; Einstein metrics, Poincare-Einstein metrics, and compactifications of certain Ricci-flat asymptotically locally Euclidean structures are…
Various types of Lagrange and Finsler geometries and the Einstein gravity theory, and modifications, can be modelled by nonholonomic distributions on tangent bundles/ manifolds when the fundamental geometric objects are adapted to nonlinear…
We generalize the algorithm that establishes the correspondence between metric-affine Eddington-inspired Born-Infeld (EiBI) gravity and General Relativity (GR) to any bosonic matter sector. Along the way, a polished version of the proof of…
The aim of this paper is to construct infinitely many families of Einstein metrics on the connected sums of arbitrary number of copies of $S^2\times S^3$. We realize these 5-manifolds as total spaces of Seifert bundles over Del Pezzo…
A scale invariant theory of gravity, containing at most two derivatives, requires, in addition to the Riemannian metric, a scalar field and (or) a gauge field. The gauge field is usualy used to construct the affine connection of Weyl…
We construct a new class of exact solutions describing spacetimes possessing Lie algebroid symmetry. They are described by generic off-diagaonal 5D metrics embedded in bosonic string gravity and possess nontrivial limits to the Einstein…
Metric-affine theories of gravity provide an interesting alternative to General Relativity: in such an approach, the metric and the affine (not necessarily symmetric) connection are independent quantities. Furthermore, the action should…
In the harmonic description of general relativity, the principle part of Einstein equations reduces to a constrained system of 10 curved space wave equations for the components of the space-time metric. We use the pseudo-differential theory…
Relying on a fundamental empirical identity of heavy and inertial mass it is proposed to bring a status of general theory of relativity (GTR) of Einstein up to a level of Unified Field Theory. To do this, a thoroughgoing revision of…
This paper is a comprehensive investigation of the Affine Gauge Theory (AGT) as a gauge theory of gravity having the same mathematical structure as gauge theories of the other fundamental forces of nature. This mathematical structure…
We present a rigorous and functorial quantization scheme for affine field theories, i.e., field theories where local spaces of solutions are affine spaces. The target framework for the quantization is the general boundary formulation,…
Metrics on Grassmannians have a wide array of applications: machine learning, wireless communication, computer vision, etc. But the available distances between subspaces of distinct dimensions present problems, and the dimensional asymmetry…
An affine hypersurface (AH) structure is a pair comprising a conformal structure and a projective structure such that for any torsion-free connection representing the projective structure the completely trace-free part of the covariant…
A new geometry, called General geometry, is constructed. It is proven that its the most simplest special case is geometry underlying Electromagnetism. Another special case is Riemannian geometry. Action for electromagnetic field and Maxwell…
The affine connection in a space-time with a maximally symmetric spatial subspace is derived using the properties of maximally symmetric tensors. The number of degrees of freedom in metric-affine gravity is thereby considerably reduced…