Riemannian manifolds with two circulant structures

TL;DR

This paper studies three-dimensional Riemannian manifolds with two circulant structures, exploring their curvature properties, providing an example, and deriving conditions for the structure to be parallel.

Contribution

It introduces a new class of manifolds with circulant structures, analyzing their curvature and parallelism conditions, which is a novel contribution in differential geometry.

Findings

Derived curvature properties of the manifold

Provided an explicit example of such a manifold

Established a condition for the structure q to be parallel

Abstract

We consider a three-dimensional Riemannian manifold equipped with two circulant structures - a metric g and a structure q, which is an isometry with respect to g and the third power of q is minus identity. We discuss some curvature properties of this manifold, we give an example of such a manifold and find a condition for q to be parallel with respect to the Riemannian connection of g.