Semiholonomical, holonomical and trivial spaces of affine connection :: IKBFU's united scientific journal editorial office

×

Login
Password
Forgot your password?
Login As
You can log in if you are registered at one of these services:
   
The real and legitimate goal of the sciences is the endowment of human life with new inventions and riches
Francis Bacon

DOI-generator Search by DOI on Crossref.org

Semiholonomical, holonomical and trivial spaces of affine connection

Author Shevchenko Yu.
Pages 43-48
Article Download
Keywords affine connection, Ricci’s identities, Bianchi’s identities, Laptev’s lemma, holonomicity, semi-holonomicity
Abstract (summary) In n-dimensional space of affine connection An,n with Cartan’s structure equations Ricci’s and Bianchi’s identities were received. Their invariance has been shown. After prolongation of the structure equations using Laptev’s lemma semiholonomical, holonomical and trivial manifolds are defined. The Ricci’s identities allowed us to prove semiholonomicity of the space An,n. This semiholonomicity preserves in the space without torsion A’n,n and in the space without curvature ‘An,n , besides the locally affine space Ά’n,n is trivial. Tensor of non-holonomicity of the space An,n is introduced. Vanishing of this tensor makes the space holonomic, H n n A . Also curvature tensor of associated space of affine connection without torsion A’n,n was introduced. It’s vanishing characterizes trivial space of affine connection, Tn n A .
References 1. Картан Э. Пространства аффинной, проективной и конформной связности. Казань, 1962.
2. Кириченко В. Ф. Дифференциально-геометрические структуры на многообразиях. М., 2003.
3. Лаптев Г. Ф. Основные инфинитезимальные структуры высших порядков на гладком многообразии // Тр. геом. семинара / ВИНИТИ. М., 1966. Т. 1. С. 139—189.
4. Лумисте Ю. Г. Матричное представление полуголономной дифференциальной группы и структурные уравнения расслоения p-кореперов // Там же. 1974. Т. 5. С. 239—257.
5. Шевченко Ю. И. Оснащения голономных и неголономных гладких многообразий. Калининград, 1998.

Back to the section