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
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
 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.