Glued linear connection on surface of the projective space

• Published in: Differential Geometry of Manifolds of Figures
• Main Author: K.V. Bashashina
• Format: Article in Journal/Newspaper
• Language: English; Russian
• Published: Immanuel Kant Baltic Federal University 2020
• Subjects: projective space surface; glued bundle; linear connection; glued linear connection; cartan projective connection; curvature tensor; Mathematics; QA1-939; laptev
• Online Access: https://doi.org/10.5922/0321-4796-2020-51-3; https://doaj.org/article/abdc193ce7da400b889ec19cf9870328

We consider a surface as a variety of centered planes in a multidi­mensional projective space. A fiber bundle of the linear coframes appears over this manifold. It is important to emphasize the fiber bundle is not the principal bundle. We called it a glued bundle of the linear coframes. A connection is set by the Laptev — Lumiste method in the fiber bundle. The ifferential equations of the connection object components have been found. This leads to a space of the glued linear connection. The expres­sions for a curvature object of the given connection are found in the pa­per. The theorem is proved that the curvature object is a tensor. A condi­tion is found under which the space of the glued linear connection turns into the space of Cartan projective connection. The study uses the Cartan — Laptev method, which is based on cal­culating external differential forms. Moreover, all considerations in the article have a local manner.