Almost conformal transformation in a class of Riemannian manifolds

TL;DR

This paper introduces a new class of almost conformal transformations in 3D Riemannian manifolds with circulant tensor structures, constructing an infinite series of related metrics and exploring their properties.

Contribution

It defines almost conformal transformations in manifolds with circulant tensors and constructs an infinite series of successively related metrics.

Findings

Constructed an infinite series of circulant metrics

Established properties of these almost conformal metrics

Extended the concept of conformal transformations in specific Riemannian manifolds

Abstract

We consider a 3-dimensional Riemannian manifold V with a metric g and an affinor 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.