Z-symmetries of a Class of Indefinite Almost Paracontact Metric Manifolds

Abstract

The primary objective of this paper is to examine the -symmetries of indefinite almost paracontact metric manifolds, with particular emphasis on three-dimensional -para Kenmotsu manifolds. We demonstrate that the Einstein manifolds and the stipulation of possessing distinct -symmetries are equivalent for three-dimensional -para Kenmotsu manifolds. It has also been deduced that a -pseudosymmetric three-dimensional -paraKenmotsu manifold exists. In the conclusion, we prove that all projectively -semisymmetric three-dimensional -para Kenmotsu manifolds are Einstein manifolds.