Almost Conformal Transformation in a Class of Riemannian Manifolds

We consider a 3-dimensional Riemannian manifold V with a metric g and an a±nor structure q. The local coordinates of these tensors are circulant matrices. In V we define an almost conformal transformation. Using that definition we construct an infinite series of circulant metrics which are successively almost conformaly related. In this case we get some properties

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

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