Open AccessAbout an analogue of Neifeld’s connection on the space of centred planes with one-index basic-fibre forms
Author(s) -
Ele. Belova,
Olga Belova
Publication year - 2019
Publication title -
differencialʹnaâ geometriâ mnogoobrazij figur
Language(s) - English
Resource type - Journals
eISSN - 2782-3229
pISSN - 0321-4796
DOI - 10.5922/0321-4796-2019-50-6
Subject(s) - fiber bundle , mathematics , tangent space , connection (principal bundle) , normalization (sociology) , space (punctuation) , plane (geometry) , mathematical analysis , pure mathematics , geometry , fiber , computer science , materials science , sociology , anthropology , composite material , operating system
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 n P . 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.