They adequately generalize the

Einstein space endowed with the cosmological constant [LAMBDA] defined as:

an

Einstein space which is Ricci-flat and consequently has zero scalar curvature, too.

The background space is not one an

Einstein space (where [R.

alpha][beta]], the associated space is called an

Einstein space.

Metric (1a) and Euclidean-like structure (1b) are complementary to each other in the

Einstein space.

From the purely geometrical perspective, an

Einstein space [5] is described by any metric obtained from

in which case the space, where the gravitational field is located, is called an

Einstein space.

The topics are notations and prerequisites from analysis, curves in Rn, the local theory of surfaces, the intrinsic geometry of surfaces, Riemannian manifolds, spaces of constant curvature, and

Einstein spaces.

Besides, Schwarzschild space is only a very particular case of

Einstein spaces of type I.

In a previous paper the writer treated of particular classes of cosmological solutions for certain

Einstein spaces and claimed that no such solutions exist in relation thereto.

Thus, it has failed to understand the geometrical structure of type 1

Einstein spaces.

This follows since it has been proved that cosmological solutions to Einstein's field equations for isotropic type 1

Einstein spaces, from which the expanding Universe and the Big Bang have allegedly been derived, do not even exist.