We study real affine hypersurfaces $f\colon M\rightarrow \mathbb{ R}^{ 2n+2}$ with an almost paracontact structure $(\varphi ,\xi,\eta)$ induced by a $\widetilde{ J}$-tangent transversal vector filed, where $\widetilde{ J}$ is the canonical paracomplex structure on $\mathbb{ R}^{ 2n+2}$. We give a classification of hypersurfaces for which an induced almost paracontact structure is metric relative to the second fundamental form. Some other properties of such hypersurfaces are also studied.
Categories: math.DG