Three-dimensional Riemannian manifolds with circulant structures

摘要

We consider a 3-dimensional Riemannian manifold M with two circulantstructures -- a metric g and an endomorphism q whose third power is identity.The structure q is compatible with g such that an isometry is induced in anytangent space of M. We obtain some curvature properties of this manifold (M, g,q) and give an explicit example of such a manifold.