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A 4-dimensional Riemannian manifold equipped with an endomorphism of thetangent bundle, whose fourth power is the identity, is considered. The matrixof this structure in some basis is circulant and the structure acts as anisometry with respect to the metric. Such manifolds are constructed on4-dimensional real Lie groups with Lie algebras of two remarkable types. Someof their geometric characteristics are obtained.

Two types of Lie Groups as 4-dimensional Riemannian manifolds with circulant structure