the main objective of this paper is to find the necessary and sufficient condition of a given finslermetric to be einstein in order to classify the einstein finsler metrics on a compact manifold. the consideredeinstein finsler metric in the study describes all different kinds of einstein metrics which are pointwiseprojective to the given one. this study has resulted in the following theorem tha...

In this paper we study the structure of standard Einstein solvmanifolds of arbitrary rank. Also the validity of a variational method for finding standard Einstein solvmanifolds is proved.

In this paper we consider an Einstein-type equation which generalizes important geometric equations, like static and critical point equations. We prove that a complete manifold with fourth-order divergence-free Weyl tensor zero radial curvature is locally warped product $(n-1)$-dimensional Einstein fibers, provided the potential function proper. As consequence, result about nonexistence of mult...

We investigate the dynamics of plane wave state in one-dimensional spin-tensor-momentum coupled Bose-Einstein condensate. By using Gaussian variational approximation, we first derive equations motion for parameters, including center-of-mass coordinate, momentum, amplitude, width, chirp, and relative phase. These parameters are together nonlinearly by coupling, Raman spin-dependent atomic intera...

The curvature tensor \(\hat{R}\) of a manifold is called harmonic, if it obeys the condition \(\Delta^{\text{(HR)}}\hat{R}=0\), where \(\Delta^{\text{(HR)}}=DD^{\ast} +
 D^{\ast}D\) Hodge–deRham Laplacian. It proved that all solutions Einstein equations in vacuum, as well Einstein–Cartan theory vacuum have harmonic curvature. statement only Einstein’s type \(N\) (describing gravitational r...

We propose to compute the action and global charges of the asymptotically de Sitter solutions in Einstein-Gauss-Bonnet theory by using the counterterms method in conjunction with the quasilocal formalism. The general expression of the counterterms and the boundary stress tensor is presented for spacetimes of dimension d ≤ 7. We apply this tehnique for several different solutions in Einstein-Gau...

The main result of this paper is that the space of conformally compact Einstein metrics on any given manifold is a smooth, infinite dimensional Banach manifold, provided it is non-empty, generalizing earlier work of Graham-Lee and Biquard. We also prove full boundary regularity for such metrics in dimension 4 and a local existence and uniqueness theorem for such metrics with prescribed metric a...

This paper is devoted to compute the energy-momentum densities for two exact solutions of the Einstein field equations by using the prescriptions of Einstein, Landau-Lifshitz, Papapetrou and Möller. The spacetimes under consideration are the Weyl-Lewis-Papapetrou and the Levi-Civita metrics. The Weyl metric becomes the special case of the Weyl-Lewis-Papapetrou solution. The Levi-Civita metric p...