On affine connections in a Riemannian manifold with a circulant metric and two circulant affinor structures

摘要

In the present paper it is considered a class V of 3-dimensional Riemannianmanifolds M with a metric g and two affinor tensors q and S. It is definedanother metric \bar{g} in M. The local coordinates of all these tensors arecirculant matrices. It is found: 1)\ a relation between curvature tensors R and \bar{R} of g and \bar{g},respectively; 2)\ an identity of the curvature tensor R of g in the case when the curvaturetensor \bar{R} vanishes; 3)\ a relation between the sectional curvature of a 2-section of the type\{x, qx\} and the scalar curvature of M.