The Grassmann-like manifold of centered planes when a surface is described by the centre
- DOI
- 10.5922/0321-4796-2021-52-4
- Pages
- 30-41
Abstract
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.
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