Conformal Equitorsion and Concircular Transformations in a Generalized Riemannian Space

In the beginning, the basic facts about a conformal transformations are exposed and then equitorsion conformal transformations are defined. For every five independent curvature tensors in Generalized Riemannian space, the above cited transformations are investigated and corresponding invariants-5 concircular tensors of concircular transformations are found.

Conformal curvature tensors in a generalized Riemannian space in Eisenhart sense

In the present paper generalizations of conformal curvature tensor from Riemannian space are given for five independent curvature tensors in generalized Riemannian space (GRN ), i.e. when the basic tensor is non-symmetric. In earlier works of S. Mincic and M. Zlatanovic et al a special case has been investigated, that is the case when in the conformal transformation the torsion remains invariant (equitorsion transformation). In the present paper this condition is not supposed and for that reason the results are more general and new.

Cosmological meaning of geometric curvatures

In this paper, we analyzed the physical meaning of scalar curvatures for a generalized Riemannian space. It is developed the Madsen?s formulae for pressures and energy-densities with respect to the corresponding energy-momentum tensors. After that, the energy-momentum tensors, pressures, energy-densities and state-parameters are analyzed with respect to different concepts of generalized Riemannian spaces. At the end of this paper, linearities of the energy-momentum tensor, pressure, energy-density and the state-parameter are examined.

Second type almost geodesic mappings of special class and their invariants

Invariants of almost geodesic mappings of a generalized Riemannian space are discussed in this paper. As a special case, invariants of equitorsion almost geodesic mappings of this type are discussed in here.

Certain properties of generalized Einstein spaces

In the present paper are introduced generalized Einstein spaces. Einstein type tensors are represented in the generalized Einstein spaces. Some relations of Einstein type tensors of the first and the second kind in the generalized Riemannian space are obtained. Also, geodesic mappings of T-connected generalized Einstein spaces onto Riemannian space are considered.