A class of indefinite almost paracontact metric manifolds

Abstract

This research, we develop a new class of indefinite almost paracontact metric manifolds, termed ($\epsilon$)-para Kenmotsu manifolds and we obtain some typical identities for the curvature tensor, scalar curvature and Ricci tensor. Furthermore, in particular, we investigate the curvature features of $three$-dimensional ($\epsilon$)-para Kenmotsu manifolds. We establish an essential as well as sufficient condition for an ($\epsilon$)-para Kenmotsu $3$-manifold to have an indefinite space form. Furthermore, we classify and demonstrate that ($\epsilon$)-para Kenmotsu $3$-manifolds, which are either semi-symmetric, Ricci-semi-symmetric or semi-symmetric type, are $\eta$-Einstein. In conclusion, we create a $3$-D ($\epsilon$)-para Kenmotsu manifold example.