  Work consists of introduction, two chapters, conclusion and four
applications. In this work is examined the condition, with which the wave space
metrics of Riemann- Cartan is the solution of Einstein equation in the void.
Geometric structures were for this purpose studied on the differentiated
variety: connectedness, curvature and twisting connectedness. For this was used
this analytical apparatus of differential geometry as the calculation of
exterior forms.
  In the first chapter the following concepts are examined: - variety; -
vectors and 1- forms on the varieties; - metric tensor, connectedness and the
covariant derivative; - form with the values in the vector spaces; - the
structural equations of Cartan. The second chapter is dedicated to the presence
of condition, during which wave certificate is the solution of Einstein
equation in the void. Using the first and second structural equations of Cartan
for the variety without twisting of that allotted by wave certificate, they
were calculated: the 1- forms of connectedness and the coefficients of
connectedness, and also Riemann tensor, Ricci tensor and scalar of curvature.
  In appendix 1 the derivation of formula for the coefficients of
connected-ness in the space with the twisting is given. In appendix 2 the
calculation of the components of the 1- forms of connectedness is carried out.
In appendix 3 the calculations of the components of the 2- forms of curvature
are presented. In appendix 4 the components of Ricci tensor are calculated.
