Generalized bilinear connection on the space of centered planes

• Published in: Differential Geometry of Manifolds of Figures
• Main Author: O.O. Belova
• Format: Article in Journal/Newspaper
• Language: English; Russian
• Published: Immanuel Kant Baltic Federal University 2022
• Subjects: projective space; space of centered planes; generalized bilinear connection; torsion; curvature; Mathematics; QA1-939; laptev
• Online Access: https://doi.org/10.5922/0321-4796-2022-53-3; https://doaj.org/article/f9b3bd0e4e9b481a8faa5188fab1a601

We continue to study the space of centered planes in projective space . In this paper, 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, curvature-torsion, and curvature. 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.