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Riemannian manifolds with two circulant structures. (English) Zbl 1309.53014

Summary: We consider a three-dimensional Riemannian manifold equipped with two circulant structures–a metric \(g\) and a structure \(q\), which is an isometry with respect to \(g\) and the third power of \(q\) is minus identity. We discuss some curvature properties of this manifold, we give an example of such a manifold and find a condition for \(q\) to be parallel with respect to the Riemannian connection of \(g\).

MSC:

53B20 Local Riemannian geometry
53C05 Connections (general theory)
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