Riemannian almost product manifolds generated by a circulant structure

TL;DR

This paper investigates 4-dimensional Riemannian manifolds with circulant structures, exploring their almost product structures, covariant derivatives, and classification within the Staikova-Gribachev framework.

Contribution

It establishes conditions linking covariant derivatives of circulant structures to the classification of almost product manifolds.

Findings

Derived relations between covariant derivatives and circulant structures

Identified conditions for manifolds to belong to specific classes

Analyzed properties of almost product manifolds with circulant structures

Abstract

A 4-dimensional Riemannian manifold equipped with a circulant structure, which is an isometry with respect to the metric and its fourth power is the identity, is considered. The almost product manifold associated with the considered manifold is studied. The relation between the covariant derivatives of the almost product structure and the circulant structure is obtained. The conditions for the covariant derivative of the circulant structure, which imply that an almost product manifold belongs to each of the basic classes of the Staikova-Gribachev classification, are given.