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.