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