About the structure of five-dimensional complexes of two-dimensional planes in projective space $P^5$ with a single developable surface

This article focuses on projective differential geometry of submanifolds of $2$-dimensional planes manifolds $G(2, 5)$ in projective space $P^5$ containing single developable surface. To study such submanifolds we use the Grassmann mapping of manifold $G(2, 5)$ of $2$-dimensional planes in projective space $P^5$ to $9$-dimensional algebraic manifold $\Omega (2, 5)$ of space $P^19$. This mapping combined with the method of external Cartan's forms and moving frame method made possible to determine the structure of considered manifolds.