The Grassmann-like manifold of centered planes when a surface is described by the centre

We continue to study of the Grassmann-like manifold of -centered planes. A special case is considered when the center de­scribes an -dimensional surface . We will denote this mani­fold by . An analogue of the strong Norden normalization of the manifold is realized. It is proved that this normalizati...

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Bibliographic Details
Published in:Differential Geometry of Manifolds of Figures
Main Author: O.O. Belova
Format: Article in Journal/Newspaper
Language:English
Russian
Published: Immanuel Kant Baltic Federal University 2021
Subjects:
Online Access:https://doi.org/10.5922/0321-4796-2021-52-4
https://doaj.org/article/25ca7e25b5d04cf389f9d7c1f50dad03
Description
Summary:We continue to study of the Grassmann-like manifold of -centered planes. A special case is considered when the center de­scribes an -dimensional surface . We will denote this mani­fold by . An analogue of the strong Norden normalization of the manifold is realized. It is proved that this normalization induces a connection in the bundle associated with the manifold . A geometric characteristic of this connection is given with the help of parallel displacements. In our research we use the Cartan method of external forms and the group-theoretical method of Laptev. These methods are used by many geometers and physicists. The Grassmann-like manifold is closely related to such a well-known and popular manifold as the Grassmann manifold. The Grassmann mani­fold is an example of a homogeneous space and forms an important fun­damental class of projective manifolds, and the projective space itself can be represented as a Grassmann manifold.