Spheres and circles in the tangent space at a point on a Riemannian manifold with respect to an indefinite metric


Georgi Dzhelepov




We consider a 3-dimensional Riemannian manifold with an additional circulant structure, whose third power is the identity. This 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 necessarily indefinite. We find equations of a sphere and equations of a circle, which are given with respect to the associated metric, in terms of the Riemannian metric.