Second-Order Tangent-Valued Forms

Polyakova, Katerina Valentinovna

doi:10.1134/s0001434619010085

Cited by 5 publications

(2 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…e ω e b (see, e.g., [49]). We will use the following terminology (see [50]): A substructure of a structure S is called simple if it is not a union of two substructures of the structure S. A simple substructure is called the simplest if it, in turn, does not have a substructure.…”

Section: Planar Generalized Affine Connectionmentioning

confidence: 99%

Generalized Affine Connections Associated with the Space of Centered Planes

Belova

2021

Mathematics

View full text Add to dashboard Cite

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.

show abstract

Section: Planar Generalized Affine Connectionmentioning

confidence: 99%

Generalized Affine Connections Associated with the Space of Centered Planes

Belova

2021

Mathematics

View full text Add to dashboard Cite

show abstract

“…Theorem 5. The reduced object Γ II coincides with the object Γ 2 only in the case (29), where the object Γ 2 gives a connection on the reduced bundle that arises at the adaptation of the moving frame to a field of the second normals.…”

Section: Reduced Connection Objectsmentioning

confidence: 99%

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

Belova

2019

Mathematics

View full text Add to dashboard Cite

The space Π of centered m-planes is considered in projective space Pn. A principal bundle isassociated with the space Π and a group connection is given on the principal bundle. The connectionis not uniquely induced at the normalization of the space Π. Semi-normalized spaces Π1, Π2 andnormalized space Π1,2 are investigated. By virtue of the Cartan–Laptev method, the dynamics ofchanges of corresponding bundles, group connection objects, curvature and torsion of the connectionsare discovered at a transition from the space Π to the normalized space Π1,2.

show abstract

The space of centered planes and generalized bilinear connection

Belova

2023

Filomat

View full text Add to dashboard Cite

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.

show abstract

Second-Order Tangent-Valued Forms

Cited by 5 publications

References 2 publications

Generalized Affine Connections Associated with the Space of Centered Planes

Generalized Affine Connections Associated with the Space of Centered Planes

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

The space of centered planes and generalized bilinear connection

Contact Info

Product

Resources

About