Geodesic
Reduction of bundles of a Grassmann-like manifold of centered planes under normalization
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 2, Tome 180 (2020), pp. 3-8

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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. 
@article{INTO_2020_180_a0,
     author = {O. Belova},
     title = {Reduction of bundles of a {Grassmann-like} manifold of centered planes under normalization},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {3--8},
     publisher = {mathdoc},
     volume = {180},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_180_a0/}
}
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O. Belova. Reduction of bundles of a Grassmann-like manifold of centered planes under normalization. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 2, Tome 180 (2020), pp. 3-8. http://geodesic.mathdoc.fr/item/INTO_2020_180_a0/