  We study hyper-spheres, spheres and circles, with respect to an indefinite
metric, in a tangent space on a 4-dimensional differentiable manifold. The
manifold is equipped with a positive definite metric and an additional tensor
structure of type (1, 1)11. The fourth power of the additional structure is
minus identity and its components form a skew-circulant matrix in some local
coordinate system. The both structures are compatible and they determine an
associated indefinite metric on the manifold.
