Almost symmetric and antisymmetric spaces with affine connection

Let (M,nabla) be an almost symmetric space. The curvature tensor R and the torsion tensor T determine the operations (xi ,eta ,zeta )=R(xi,eta)zeta and xicdoteta=frac{1}{2}T(xi ,eta) in Tsb e(M) (ein M), respectively. These operations are connected by the rule (xi ,eta,zeta cdotkappa )=(xi ,eta,zeta) cdotkappa+zetacdot (xi ,eta,kappa ). The authors prove that the local structure of an almost symmetric space (M,nabla) in a neighbourhood of ein M is uniquely determined by (Tsb e(M),( ),cdot), where ( ) and cdot satisfy the above relation. par The analogous problem for antisymmetric spaces is also considered.

Authors
Sabinin L.V. , Mikheev P.O.
Editors
Kovacs Zoltan
Number of issue
no.~1
Language
English, Russian
Status
Published
Year
1994
Date of creation
19.05.2021
Date of change
19.05.2021
Short link
https://repository.rudn.ru/en/records/article/record/73848/
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Mikheev P.O., Sabinina Liudmila
Успехи математических наук. Федеральное государственное бюджетное учреждение науки Математический институт им. В.А. Стеклова Российской академии наук. 1994.