Related papers: Around a theory of a Walker spaces

An examples of the Ricci-flat metric associated with the equations of Navier-Stokes are constructed. Their properties are investigated.

An examples of multidimensional the Ricci-flat spaces defined by nonlinear differential equations are constructed. Their properties are discussed.

Generalized differential forms are used in discussions of metric geometries and Einstein's vacuum field equations. Cartan's structure equations are generalized and applied. In particular flat generalized connections are associated with any…

We construct an example of Ricci-flat almost-K\"ahler non-K\"ahler structure in four dimensions.

In this paper we study the invariant Walker structures over the conformally flat four-dimensional homogeneous manifolds according to the Seger types of the Ricci operator.

This paper constructs a Riemann surface associated to the icosahedron and discusses the geodesics associated to a flat metric on this surface. Because of the icosahedral symmetry, this is a distinguished special case of the example treated…

We consider four dimensional spaces of neutral signature and give examples of universal spaces of Walker type. These spaces have no analogue in other signatures in four dimensions and provide with a new class of spaces being universal.

The purpose of the present article is to study and characterize sev- eral types of symmetries of generalized Robertson-Walker space-times. Con- formal vector fields, curvature and Ricci collineations are studied. Many im- plications for…

We classify generalized Wallach spaces which are g.o. spaces. We also investigate homogeneous geodesics in generalized Wallach spaces for any given invariant Riemannian metric and we give some examples.

We employ a theorem due to Campbell to build some simple 4-dimensional cosmological models which originate from solutions describing waves propagating along the extra-dimension of a 5-dimensional Ricci-flat space. The dimensional reduction…

We define a class of two dimensional surfaces conformally related to minimal surfaces in flat three dimensional geometries. By the utility of the metrics of such surfaces we give a construction of the metrics of $2 N$ dimensional Ricci flat…

A generalization of metric space is presented which is shown to admit a theory strongly related to that of ordinary metric spaces. To avoid the topological effects related to dropping any of the axioms of metric space, first a new, and…

We study relation of the Ricci Flow on 3-dimensional Lie groups and 4-dimensional Ricci-flat manifolds. In particular, we construct Ricci-flat cohomogeneity one metrics with respect to 3-dimensional Lie groups.

We establish a 1-to-1 relation between metrics on compact Riemann surfaces without boundary, and mechanical systems having those surfaces as configuration spaces.

Ricci-flat metrics of the ultrahyperbolic signature which enjoy the l-conformal Galilei symmetry are constructed. They involve the AdS_2-metric in a way similar to the near horizon black hole geometries. The associated geodesic equations…

We study the behavior of a three-dimensional dynamical system with respect to some set $S$ given in 3-dimensional euclidian space. Geometrically such a system arises from the normalized Ricci flow on some class of generalized Wallach spaces…

In this paper, we investigate geometric properties of some curvature tensors of a four-dimensional Walker manifold. Some characterization theorems are also obtained.

In this paper, four parameters Wright function is considered. Certain geometric properties such as starlikeness, convexity, uniform convexity and close-to-convexity are discussed for this function. Further, certain geometric properties of…

Some examples of ten-dimensional vacuum Einstein spaces made up on basis of four-dimensional Ricci-flat spaces and six-dimensional Ricci-flat spaces defined by solutions of the Sin-Gordon equation are constructed. The properties of…

We study an even dimensional manifold with a pseudo-Riemannian metric with arbitrary signature and arbitrary dimensions. We consider the Ricci flat equations and present a procedure to construct solutions to some higher (even) dimensional…