Automorphisms of Riemann-Cartan manifolds

It is proved that the maximal dimension of the Lie group of automorphisms of an n-dimensional Riemann-Cartan manifold (space) (M (n) , g, ) equals n(n - 1)/2+ 1 for n > 4 and, if the connection is semisymmetric, for n a parts per thousand yen 2. If n = 3, then the maximal dimension of the group equals 6. Three-dimensional Riemann-Cartan spaces (M (3), g, ) with automorphism group of maximal dimension are studied: the torsion s and the curvature are introduced, and it is proved that s and are characteristic constants of the space and = k - s (2), where k is the sectional curvature of the Riemannian space (M (3), g); a geometric interpretation of torsion is given. For Riemann-Cartan spaces with antisymmetric connection, the notion of torsion at a given point in a given three-dimensional direction is introduced.