Geodesic
On Affine Connections in a Riemannian Manifold with a Circulant Metric and two Circulant Affinor Structures
Mathematics and Education in Mathematics, Tome 40 (2011) no. 1, pp. 176-181.

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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 ¯g in M. The local coordinates of all these tensors are circulant matrices. It is found: 1) a relation between curvature tensors R and ¯R of g and ¯g, respectively; 2) an identity of the curvature tensor R of g in the case when the curvature tensor ¯R vanishes; 3) a relation between the sectional curvature of a 2-section of the type {x, qx} and the scalar curvature of M. *2000 Mathematics Subject Classification: 53C15, 53B20.
Keywords: Riemannian Manifold, Affinor Structure, Curvatures 
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     title = {On {Affine} {Connections} in a {Riemannian} {Manifold} with a {Circulant} {Metric} and two {Circulant} {Affinor} {Structures}},
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Dokuzova, Iva; Razpopov, Dimitar. On Affine Connections in a Riemannian Manifold with a Circulant Metric and two Circulant Affinor Structures. Mathematics and Education in Mathematics, Tome 40 (2011) no. 1, pp. 176-181. http://geodesic.mathdoc.fr/item/MEM_2011_40_1_a14/