Some results on almost paracontact paracomplex Riemannian manifolds

In this study, a class of Riemannian almost product manifolds is obtained by the warped product of almost paracontact paracomplex Riemannian manifolds with $\mathbb{R}$. The curvature properties of the almost product manifolds are studied. Then, normal almost paracontact paracomplex Riemannian manifolds are considered. It is proven that the almost paracontact paracomplex Riemannian manifolds are normal if and only if the almost product manifolds obtained by the warped product are integrable. In addition, examples of almost paracont paracomplex Riemannian manifolds are given.