Abstract:
In the projective space $P_n$, we consider the Grassmann-like manifold $Gr^*(m,n)$ of centered planes and the associated principal bundle. We perform the normalization of the manifold $Gr^*(m,n)$ by the normal fields of the first and second orders and the the adaptation of the bundle corresponding to these normals. Semi-normalized spaces of the first and second kind and the normalized space are examined. The dynamics of changes of the corresponding bundles is established when passing from the space $Gr^*(m,n)$ to the normalized space.
Keywords:Cartan–Laptev method, Grassmann-like manifold of centered planes, normalization, reduction.