TO PROJECTIVE DIFFERENTIAL GEOMETRY OF 5–DIMENSIONAL COMPLEXES 2–DIMENSIONAL PLANES IN PROJECTIVE SPACE P5

The article focuses on the differential geometry  of 5-dimensional complexes  C5 of 2-dimensional planes in projective  space  P5 that contains a finite  number developable surfaces. This relates to researches projective geometry based E. Cartan’s moving frame method and exterior forms. These methods make it possible study submanifolds different dimensions Grassmann manifold from single viewpoint also extend results wider classes manifolds multidimensional planes. In order such submanifolds, we apply mapping manifold  G(2, 5) onto 9-dimensional algebraic Ω(2, space P19. main task is carry out uniform classifications various determine their structure define degree arbitrariness existence research properties classes. Intersection with its tangent TlΩ(2, 5) represents Segre cone Cl(3, 3). carries two sets plane 3-dimensional generatrices intersecting straight lines. projectivization PBl(2) of this Sl(2, 2). 2) is invariant under transformations P8 = PTlΩ(2, 5), which center at point l 5) to 5). used for classification consideration, as well interpretation properties  terms.  classification  is  on  various  configurations 5) and 2).  goal article  prove geometrically theorem determination