Investigation of conformal deformations of almost parachermitian structures obtained from almost parakontact metric structures

In this study, almost parahermitian manifolds obtained from conformal deformations of almost paracontact metric manifolds and almost paracontact metric manifolds obtained from almost parahermitian manifolds are considered. Any almost paracontact metric manifold is multiplied by R (real numbers) and an almost parahermitian structure is constructed on M × R using the function e2σ , whereσ : M × R −→ R, σ(X, t) = t. Then the relations between the classes of M and M × R are studied. In addition, two different almost paracontact metric structures are obtained on N × R from any almost parahermitian metric manifold N by using two different metrics, one of which depends on σ : N × R −→ R, σ(X, t) = t. It is also shown that if the manifold N is Einstein (Ricci soliton, Yamabe soliton), then the manifold N ×R is η-Ricci soliton (η-Ricci soliton, quasi Yamabe soliton). Finally, the relations between the classes of N and N × R are investigated and using the relations obtained in the study, examples of various classes of almost paracontact metric manifolds and almost parahermitian manifolds are presented.