Three classes of Weitzenbock manifolds
The Weitzenbock manifold is the triplet defined by a differential manifold with the metric g of a certain signature and linear connection of zero curvature tensor, the nonzero torsion tensor, and the metricity property. The theory of such manifolds is called the "new theory of gravity". We consider properties of three classes of such manifolds and on this base prove the vanishing thorems.