  We consider a $3$-dimensional differentiable manifold with two circulant
structures -- a Riemannian metric and an additional structure, whose third
power is the identity. The structure is compatible with the metric such that an
isometry is induced in any tangent space of the manifold. Further, we consider
an associated metric with the Riemannian metric, which is necessary indefinite.
We find equations of a sphere and of a circle, which are given in terms of the
associated metric, with respect to the Riemannian metric.
