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A nonlocal generalization of Einstein's theory of gravitation is constructed within the framework of the translational gauge theory of gravity. In the linear approximation, the nonlocal theory can be interpreted as linearized general…
A new framework to perturbative quantum gravity is proposed following the geometry of nonholonomic distributions on (pseudo) Riemannian manifolds. There are considered such distributions and adapted connections, also completely defined by a…
We develop the basics of a theory of almost isometries for spaces endowed with a quasi-metric. The case of non-reversible Finsler (more specifically, Randers) metrics is of particular interest, and it is studied in more detail. The main…
A covariant reformulation of General Relativity is briefly considered from three points of view: geometrodynamics, Lagrange-Euler field theory, and gauge field theory. From a geometrodynamics perspective, a definition of the reference frame…
Over the last seventy years, many Finsler-type geometric and modified gravity theories have been elaborated. They have been formulated in terms of different classes of Finsler generating functions, metric and nonmetric structures, nonlinear…
The general notion of anisotropic connections $\nabla$ is revisited, including its precise relations with the standard setting of pseudo-Finsler metrics, i.e., the canonic nonlinear connection and the (linear) Finslerian connections. In…
The analysis of measurements of accelerated observers in Minkowski spacetime has led to the development of nonlocal special relativity theory. Inertia and gravitation are intimately connected in accordance with the principle of equivalence.…
We survey the geometry of Lagrange and Finsler spaces and discuss the issues related to the definition of curvature of nonholonomic manifolds enabled with nonlinear connection structure. It is proved that any commutative Riemannian geometry…
In this work a proposal for definition of twistors on generic curved spaces is exposed and investigated. We consider superpositions of nearly autoparallel and nearly geodesic maps (nearly conformal maps, nc-maps) of (pseudo-)Riemannian…
We apply the method of moving anholonomic frames in order to construct new classes of solutions of the Einstein equations on (2+1)-dimensional pseudo-Riemannian spaces. There are investigated black holes with deformed horizons and…
Modified gravity theories (MGTs) have long been studied as alternatives to general relativity (GR) and the standard Lambda CDM cosmological model. For example, exponential f(R) models often yield better fits to observational data,…
The Hamiltonian approach to the General Relativity is formulated as a joint nonlinear realization of conformal and affine symmetries by means of the Dirac scalar dilaton and the Maurer-Cartan forms. The dominance of the Casimir vacuum…
The space of anisotropic $r$-contravariant $s$-covariant $\alpha$-homogeneous tensors on a manifold admits a functorial structure where vertical derivatives $\dot{\partial}$ and contractions $\imath_{\mathbb{C}}$ by the Liouville vector…
We generalize the geometry of Santilli's locally anisotropic and inhomogeneous isospaces to the geometry of vector isobundles provided with nonlinear and distinguished isoconnections and isometric structures. We present, apparently for the…
We briefly discuss new models of an `affine' theory of gravity in multidimensional space-times with symmetric connections. We use and generalize Einstein's proposal to specify the space-time geometry by use of the Hamilton principle to…
Using our anholonomic frame deformation method, we show how generic off-diagonal cosmological solutions depending, in general, on all spacetime coordinates and undergoing a phase of ultra-slow contraction can be constructed in massive…
We model pseudo-Finsler geometries, with pseudo-Euclidean signatures of metrics, for two classes of four dimensional nonholonomic manifolds: a) tangent bundles with two dimensional base manifolds and b) pseudo-Riemannian/ Einstein…
In this paper we analyze the conditions when the Einstein equations with cosmological constant and matter describe (2+1)-dimensional generic locally anisotropic (la) spacetimes of generalized Finsler type. New classes of solutions for such…
We outline an unified approach to geometrization of Lagrange mechanics, Finsler geometry and geometric methods of constructing exact solutions with generic off-diagonal terms and nonholonomic variables in gravity theories. Such geometries…
We present an introduction to the geometry of higher order vector and co--vector bundles (including higher order generalizations of the Finsler geometry and Kaluza--Klein gravity) and review the basic results on Clifford and spinor…