A note on the existence of proper weakly cyclic $Z$ symmetric manifolds

TL;DR

This paper investigates the defining conditions of weakly cyclic Ricci symmetric and Z-symmetric manifolds, exploring their existence through proper examples to clarify their geometric properties.

Contribution

It introduces the defining conditions of weakly cyclic Ricci symmetric and Z-symmetric manifolds and provides proper examples demonstrating their existence.

Findings

Existence of proper weakly cyclic Ricci symmetric manifolds

Existence of proper weakly cyclic Z-symmetric manifolds

Clarification of the geometric properties of these manifolds

Abstract

The object of the present note is to discuss about the defining condition of weakly cyclic Ricci symmetric manifolds and weakly cyclic $Z$-symmetric manifolds \cite{DMS15} and the existence of such notion by proper examples.