About differential equations of the curvature tensors of a fundamental group and affine connections

• Published in: Differential Geometry of Manifolds of Figures
• Main Author: N. Ryazanov
• Format: Article in Journal/Newspaper
• Language: English; Russian
• Published: Immanuel Kant Baltic Federal University 2019
• Subjects: structure equations of laptev; fundamental-group connec­tion; affine connection; connection object; curvature tensor; Mathematics; QA1-939; Lemma; laptev
• Online Access: https://doi.org/10.5922/0321-4796-2019-50-15; https://doaj.org/article/1f31faf8ca8a4b1f84e8179cd12516ec

The principal bundle is considered, the base of which is an n-dimen­sional smooth manifold, and the typical fiber is an r-fold Lie group. Struc­ture equations for the forms of the fundamental group and affine connec­tions are given, each of which contains the corresponding compo­nents of the curvatu...