$\widetilde{J}$-tangent affine hypersurfaces with an induced almost paracontact structure

TL;DR

This paper classifies certain affine hypersurfaces in real space with an induced almost paracontact structure derived from a canonical paracomplex structure, exploring their properties and metric conditions.

Contribution

It provides a classification of $ ilde{J}$-tangent affine hypersurfaces with metric almost paracontact structures and investigates their geometric properties.

Findings

Classification of hypersurfaces with induced almost paracontact structures.

Conditions under which the structure is metric relative to the second fundamental form.

Additional geometric properties of these hypersurfaces.

Abstract

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.