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

Дифференциальная геометрия многообразий фигур

O. Belova¹  Е. Belova¹ 

[1] Immanuel Kant Baltic Federal University;

关键词: projective space;    space of centred planes;    analogue of norden strong normalization;    neifeld’s connection;   

DOI  :  10.5922/0321-4796-2019-50-6

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown