Reduction of Bundles, Connection, Curvature, and Torsion of the Centered Planes Space at Normalization

Belova, Olga

doi:10.3390/math7100901

Cited by 2 publications

(1 citation statement)

References 15 publications

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“…Principal fibering with gluing to the base was introduced in the paper [32] and generalized principal fibering (a principal fibering with semi-gluing to the base) was introduced in the paper [33]. Connections in the fiberings associated with the space of centered planes were studied in [34,35]. In the present paper, generalized affine connections associated with this space are considered.…”

Section: Introductionmentioning

confidence: 99%

Generalized Affine Connections Associated with the Space of Centered Planes

Belova

2021

Mathematics

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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.

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Section: Introductionmentioning

confidence: 99%

Generalized Affine Connections Associated with the Space of Centered Planes

Belova

2021

Mathematics

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The space of centered planes and generalized bilinear connection

Belova

2023

Filomat

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We continue to study the space of centered planes in n-dimension projective space. We use E. Cartan?s method of external forms and the group-theoretical method of G. F. Laptev to study the space of centered planes of the same dimension. These methods are successfully applied in physics. In a generalized bundle, a bilinear connection associated with a space is given. The connection object contains two simplest subtensors and subquasi-tensors (four simplest and three simple subquasi-tensors). The object field of this connection defines the objects of torsion S, curvature-torsion T, and curvature R. The curvature tensor contains six simplest and four simple subtensors, and curvature-torsion tensor contains three simplest and two simple subtensors. The canonical case of a generalized bilinear connection is considered. We realize the strong Lumiste?s affine clothing (it is an analog of the strong Norde?s normalization of the space of centered planes). Covariant differentials and covariant derivatives of the clothing quasi-tensor are described. The covariant derivatives do not form a tensor. We present a geometrical characterization of the generalized bilinear connection using mappings.

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Reduction of Bundles, Connection, Curvature, and Torsion of the Centered Planes Space at Normalization

Cited by 2 publications

References 15 publications

Generalized Affine Connections Associated with the Space of Centered Planes

Generalized Affine Connections Associated with the Space of Centered Planes

The space of centered planes and generalized bilinear connection

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