On pseudo-Riemannian manifolds with recurrent concircular curvature tensor

TL;DR

This paper proves that in pseudo-Riemannian manifolds, the condition of concircular recurrence implies recurrence, establishing a fundamental link between these geometric properties.

Contribution

The paper demonstrates that concircular recurrence necessarily leads to recurrence in pseudo-Riemannian manifolds, clarifying their geometric relationship.

Findings

Concircularly recurrent manifolds are necessarily recurrent.

Recurrent manifolds encompass concircularly recurrent manifolds.

The result applies to pseudo-Riemannian manifolds.

Abstract

It is proved that every concircularly recurrent manifold must be necessarily a recurrent manifold.