Abstract
Our purpose is to study a space Π of centered m-planes in n-projective space. Generalized fiberings (with semi-gluing) are investigated. Planar and normal affine connections associated with the space Π are set in the generalized fiberings. Fields of these affine connection objects define torsion and curvature tensors. The canonical cases of planar and normal generalized affine connections are considered.
Highlights
In the present paper, generalized affine connections associated with this space are considered
To define an affine connection in the generalized bundle Am2 +[m] (Π), we extend to it the Laptev–Lumiste method of defining group connections in principal bundles
This paper studied planar and normal generalized affine connections, which are associated with the space of centered planes in projective space Pn
Summary
Affine Connections Associated with the Space of Centered Planes. Weyl introduced the concept of a space of the affine connection [2]. In [9], Laptev gave an invariant definition of connections as a certain law defining the mapping of infinitely close fibres He provided a well-known theoretical-group method on the basis of the Cartan calculation. In the present paper, generalized affine connections associated with this space are considered. All known types of physical interactions (gravitational, electromagnetic, etc.) are described in terms of connections and other geometric structures on vector/principal bundles on underlying manifolds. The important role of the affine connections and the previous author’s work in the study of manifolds of planes was the motivation for writing this paper.
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