On the differential geometry of complexes of two-dimensional planes of the projective space $P^n$ containing a finite number of torsos and characterized by the configuration of their characteristic lines

This paper is devoted to the differential geometry of complexes of two-dimensional planes in the projective space $P^n$ containing a finite number of torsos. We find a necessary condition under which the complex $C^\rho$ contains a finite number of torsos, examine the properties of complexes of two-dimensional planes, which are determined by a special configuration of characteristic straight torsos belonging to the complex, and establish the structure and conditions for the existence of such complexes. The self-duality of such complexes is determined.