Affine transformations of a manifold with linear connection, and automorphisms of linear algebras. (English. Russian original) Zbl 1074.53009

Sultanov, A. Ya.

Russ. Math. 47, No. 11, 73-77 (2003); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2003, No. 11, 77-81 (2003).

Summary: We show that the group of affine transformations of a manifold \(M_n\) with linear connection \(\nabla\) induces in each tangent space \(T_{x_0}(M_n)\) of \(M_n\) a group of automorphisms of the linear algebra \(A\) with operations generated by the covariant differentials of the torsion and curvature tensor fields of \(\nabla\). The study of the automorphism group of this algebra allows us to estimate the dimension of the group of affine transformations of the space \((M_n,\nabla)\).

MSC:

53B05

Linear and affine connections