A method, due tó Elie Cartan, is used to give an algebraic classification of the non-reductive homogeneous pseudo-Riemannian manifolds of dimension four. Only one case with Lorentz signature can be Einstein without having constant curvature, and two cases with (2,2) signature are Einstein of which one is Ricci-flat. If a four-dimensional non-reductive homogeneous pseudo-Riemannian manifold is s...

A method, due tó Elie Cartan, is used to give an algebraic classification of the non-reductive homogeneous pseudo-Riemannian manifolds of dimension four. Only one case with Lorentz signature can be Einstein without having constant curvature, and two cases with (2,2) signature are Einstein of which one is Ricci-flat. If a four-dimensional non-reductive homogeneous pseudo-Riemannian manifold is s...

In this paper we study a special family of Lorentz gas with infinite horizon. The periodic scatterers have C3 smooth boundary with positive curvature except on finitely many flat points. In addition there exists a trajectory with infinite free path and tangentially touching the scatterers only at some flat points. The singularity set of the system is analyzed in detail. And we prove that the fr...

We prove the theorem valid for (Pseudo)-Riemannian manifolds Vn: ”Let x ∈ Vn be a fixed point of a homothetic motion which is not an isometry then all curvature invariants vanish at x.” and get the Corollary: ”All curvature invariants of the plane wave metric ds = 2 du dv + a(u) dw + b(u) dz identically vanish.” Analysing the proof we see: The fact that for definite signature flatness can be ch...

The object of this paper is to study $(epsilon)$-Lorentzian para-Sasakian manifolds. Some typical identities for the curvature tensor and the Ricci tensor of $(epsilon)$-Lorentzian para-Sasakian manifold are investigated. Further, we study globally $phi$-Ricci symmetric and weakly $phi$-Ricci symmetric $(epsilon)$-Lorentzian para-Sasakian manifolds and obtain interesting results.

commutative properties of four-dimensional generalized symmetric pseudo-riemannian manifolds were considered. specially, in this paper, we studied skew-tsankov and jacobi-tsankov conditions in 4-dimensional pseudo-riemannian generalized symmetric manifolds.

In this article, the impact of input pump profile on the gain spectrum as well as the saturation behavior of one-pump fiber optical parametric amplifiers (FOPAs) is investigated. Since in practical circumstances, pump sources used for FOPAs have Lorentz-Gaussian profile instead of Gaussian, a more realistic case is considered for simulating FOPAs in this article. The results of simulations for ...

in this paper, we obtain two intrinsic integral inequalities of hessian manifolds.