Parallel almost paracontact structures on affine hypersurfaces

Zuzanna Szancer

Abstract

Let J˜ be the canonical paracomplex structure on R2n+2≃C˜n+1. We study real affine hypersurfaces f:M→C˜n+1 with a J˜-tangent transversal vector field. Such a vector field induces in a natural way an almost paracontact structure (φ,ξ,η) on M as well as an affine connection ∇. In this paper we give a classification of hypersurfaces with the property that φ or η is parallel relative to the connection ∇. Moreover, we show that if ∇φ=0 (respectively ∇η=0) then around each point of M there exists a parallel almost paracontact structure. We illustrate the results with appropriate examples.
Author Zuzanna Szancer (FoEEaLS / DoAM)
Zuzanna Szancer,,
- Department of Applied Mathematics
Journal seriesAnnales Polonici Mathematici, ISSN 0066-2216, e-ISSN 1730-6272, (N/A 70 pkt)
Issue year2019
Vol122
Pages249-265
Publication size in sheets0.8
ASJC Classification2600 General Mathematics
DOIDOI:10.4064/ap180527-6-12
URL https://www.impan.pl/en/publishing-house/journals-and-series/annales-polonici-mathematici/online/113018/parallel-almost-paracontact-structures-on-affine-hypersurfaces
Languageen angielski
Score (nominal)70
Score sourcejournalList
Publication indicators WoS Citations = 0; Scopus SNIP (Source Normalised Impact per Paper): 2018 = 0.506; WoS Impact Factor: 2018 = 0.5 (2) - 2018=0.463 (5)
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