Open AccessThe Grassmann-like manifold of centered planes when a surface is described by the centre
Author(s) -
Olga Belova
Publication year - 2021
Publication title -
differencialʹnaâ geometriâ mnogoobrazij figur
Language(s) - English
Resource type - Journals
eISSN - 2782-3229
pISSN - 0321-4796
DOI - 10.5922/0321-4796-2021-52-4
Subject(s) - grassmannian , mathematics , manifold (fluid mechanics) , closed manifold , pure mathematics , connection (principal bundle) , normalization (sociology) , 3 manifold , projective space , invariant manifold , algebra over a field , projective test , geometry , mechanical engineering , sociology , anthropology , engineering
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.