相关论文: Nonholonomic Deformations of Disk Solutions and Al…

In this paper we examine a new class of five dimensional (5D) exact solutions in extra dimension gravity possessing Lie algebroid symmetry. The constructions provide a motivation for the theory of Clifford nonholonomic algebroids elaborated…

In this work, we apply the anholonomic deformation method for constructing new classes of anisotropic cosmological solutions in Einstein gravity and/or generalizations with nonholonomic variables. There are analyzed four types of, in…

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…

There are explored off-diagonal deformations of "prime" metrics in Einstein gravity (for instance, for wormhole configurations) into "target" exact solutions in f(R,T)-modified and massive/ bi-metric gravity theories. The new classes of…

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…

A generalized geometric method is developed for constructing exact solutions of gravitational field equations in Einstein theory and generalizations. First, we apply the formalism of nonholonomic frame deformations (formally considered for…

We show how the Einstein equations with cosmological constant (and/or various types of matter field sources) can be integrated in a very general form following the anholonomic deformation method for constructing exact solutions in four and…

We present new classes of exact solutions with noncommutative symmetries constructed in vacuum Einstein gravity (in general, with nonzero cosmological constant), five dimensional (5D) gravity and (anti) de Sitter gauge gravity. Such…

We find general parameterizations for generic off-diagonal spacetime metrics and matter sources in general relativity (GR) and modified gravity theories when the field equations decouple with respect to certain types of nonholonomic frames…

We propose a new framework for constructing geometric and physical models on nonholonomic manifolds provided both with Clifford -- Lie algebroid symmetry and nonlinear connection structure. Explicit parametrizations of generic off-diagonal…

We prove that the Einstein equations can be solved in a very general form for arbitrary spacetime dimensions and various types of vacuum and non-vacuum cases following a geometric method of anholonomic frame deformations for constructing…

Let $\mathbf{g}$ be a pseudo--Riemanian metric of arbitrary signature on a manifold $\mathbf{V}$ with conventional $n+n$ dimensional splitting, $\ n\geq 2,$ determined by a nonholonomic (non--integrable) distribution $\mathcal{N}$ defining…

We elaborate an unified geometric approach to classical mechanics, Riemann-Finsler spaces and gravity theories on Lie algebroids provided with nonlinear connection (N-connection) structure. There are investigated the conditions when the…

For (2+2)-dimensional nonholonomic distributions, the physical information contained into a spacetime (pseudo) Riemannian metric can be encoded equivalently into new types of geometric structures and linear connections constructed as…

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…

A new method of construction of integral varieties of Einstein equations in three dimensional (3D) and 4D gravity is presented whereby, under corresponding redefinition of physical values with respect to anholonomic frames of reference with…

In this paper we use the anholonomic frames method to construct exact solutions for vacuum 5D gravity with metrics having off-diagonal components. The solutions are in general anisotropic and possess interesting features such as an…

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,…

It is formulated a new 'anholonomic frame' method of constructing exact solutions of Einstein equations with off--diagonal metrics in 4D and 5D gravity. The previous approaches and results are summarized and generalized as three theorems…

We construct new classes of exact solutions in metric--affine gravity (MAG) with string corrections by the antisymmetric $H$--field. The solutions are parametrized by generic off--diagonal metrics possessing noncommutative symmetry…