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

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

2010-10-27

arxiv.org/abs/1010.5728v1

Proceedings of the Fortieth Jubilee Spring Conference of UBM, Borovets, (2011), 176--181,

Mathematics

Differential Geometry

Scientific paper

In the present paper it is considered a class V of 3-dimensional Riemannian manifolds M with a metric g and two affinor tensors q and S. It is defined another metric \bar{g} in M. The local coordinates of all these tensors are circulant 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 curvature tensor \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.

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