We obtain on a Kähler B-manifold (i.e., manifold with Norden metric) some corresponding results from the Kählerian and para-Kählerian context concerning Bochner curvature. prove that such is of constant totally real sectional curvatures if only it holomorphic Einstein, flat manifold. Moreover, we provide necessary sufficient conditions for gradient Ricci soliton or ?-Einstein metric to be flat....

We construct a continuous family of new homogeneous Einstein spaces with negative Ricci curvature, obtained by deforming from the quaternionic hyperbolic space of real dimension 12. We give an explicit description of this family, which is made up of Einstein solvmanifolds which share the same algebraic structure (eigenvalue type) as the rank one symmetric space HH. This deformation includes a c...

(m,?)-quasi-Einstein N(k)-contact metric manifolds have been studied and it is established that if such a manifold manifold, then the of constant sectional curvature k. Further analysis has done for gradient Einstein soliton, in particular. Obtained results are supported by an illustrative example.

— We present a detailed discussion of the inflationary scenario in the context of inhomogeneous cosmologies. After a review of the fundamental features characterizing the inflationary model, as referred to a homogeneous and isotropic Universe, we develop a generalization in view of including small inhomogeneous corrections in the theory. A second step in our discussion is devoted to show that t...

We review the finding that the general solution of many physically relevant (bosonic) Einstein-matter systems in the vicinity of a cosmological, i.e. space-like, singularity exhibit a remarkable mixture of chaos and symmetry. On the one hand, the asymptotic behavior, as one approaches the singularity, of the general solution is found to be describable, at each (generic) spatial point, as a bill...

In cite{Kats84}, Katsaras introduced a method for constructing a Hu-tton $[0,1]$-quasi-uniformity from a crisp uniformity. In this paper we present other different methods for making this based mainly in the concept of a fuzzy uniform structure. Furthermore, we prove that some of these methods preserve the completeness property of the quasi-uniformity.  Moreover, we also show that Katsaras' con...