On the existence of para-Kenmotsu manifolds

TL;DR

This paper critically examines the definition of para-Kenmotsu manifolds, identifies a fundamental flaw in its original formulation, and proves that such manifolds cannot exist under the given conditions.

Contribution

It clarifies a key issue in the definition of para-Kenmotsu manifolds and proves their non-existence under the original conditions.

Findings

The condition (2.7) in the original definition is nonsensical.

Para-Kenmotsu manifolds do not exist under the specified condition.

The paper clarifies the conceptual flaw in the existing literature.

Abstract

This note provides a quite obvious observation that the condition (2.7), which is a part of the original definition of the so-called para-Kenmotsu manifolds [9], does not make sense, and thus this concept is void. So, it is proved that the para-Kenmotsu manifolds does not exist under the condition mentioned above.