The Multidimensional Directed Euler Tour of Cubic Manifold

In the paper [3] we tried to generalize the problem of existence of a directed $(n-1)$-dimensional Euler tour for the abstract directed $n$-dimensional manifold, which is a complex of multi-ary relations [5], namely by means of abstract simplexes. In the paper [3] we show the existence of such kind of tour only for manifolds of odd dimension because we have not enough conditions to do more. In the present paper we will show conditions of existence for a directed Euler tour of abstract manifolds with even dimensions. In this purpose, we will introduce some new definitions which permit us to define manifolds by so-called abstract cubes.