SPHERES AND CIRCLES WITH RESPECT TO AN INDEFINITE METRIC ON A RIEMANNIAN MANIFOLD WITH A SKEW-CIRCULANT STRUCTURE

Abstract

We study hyper-spheres, spheres and circles, with respect to an indefinite metric, in a single 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). 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.