\widetildeJ-tangent affine hypersurfaces with an induced almost paracontact structure

2017/10/28 by Zuzanna Szancer, Szancer, Zuzanna
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.1710.10488

arxiv created 2017/10/28 · openalex publication_date 2017/10/28 · arxiv updated 2017/10/31 · openalex created_date 2017/11/10 · openalex updated_date 2026/07/28

Abstract

We study real affine hypersurfaces f\colon M→ ℝ²ⁿ⁺² with an almost paracontact structure (φ,ξ,η) induced by a \widetildeJ-tangent transversal vector filed, where \widetildeJ is the canonical paracomplex structure on ℝ²ⁿ⁺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.

Related

• Parallel Almost Paracontact Structures on Affine Hypersurfaces
• Generalized almost paracontact structures
• Almost para-Hermitian and almost paracontact metric structures induced by natural Riemann extensions
• On \widetildeJ-tangent affine hyperspheres
• Lifts of Almost r-Contact and r-Paracontact Structures