About an analogue of Neifeld’s connection on the space of centred planes with one-index basic-fibre forms

Abstract

This research is realized by Cartan — Laptev method (with prolonga­tions and scopes, moving frame and exterior forms). In this paper we con­sider a space П of centered m-planes (a space of all centered planes of the dimension m). This space is considered in the projective space . For the space П we have: dim П=n + (n – m)m. Principal fiber bundle is arised above it. The Lie group is a typical fiber of the principal fiber. This group acts in the tangent space to the П. Analogue of Neifeld’s connec­tion with multivariate glueing is given in this fibering by Laptev — Lu­miste way. The case when one-index forms are basic-fibre forms is con­sidered. We realize an analogue of the Norden strong normalization of the space П by fields of the geometrical images: (n – m – 1)-plane which is not having the common points with a centered m-plane and (m – 1)-pla­ne which is belonging to the m-plane and not passing through its centre. It is proved that the analog of the Norden strong normalization of the space of cen­tered planes induces this connection.

Keywords

• projective space
• space of centred planes
• analogue of norden strong normalization
• neifeld’s connection