On geometry of orbits of vector fields

As is known, a vector field is one of the basic concepts of geometry. In problems of the qualitative theory of differential equations, control theory, foliation theory, as well as in problems of mechanics, vector fields play an important role. This paper studies the geometry of orbits of two vector fields in four-dimensional space. The geometry of the singular foliation generated by the orbits of these vector fields is described. It is shown that the regular leaf of this foliation is a two-dimensional surface of non-zero normal curvature and nonzero Gauss torsion.