Parallel Almost Paracontact Structures on Affine Hypersurfaces

2018/05/17 by Zuzanna Szancer, Szancer, Zuzanna
Mathematics · #53A15 #53D15 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53A15 #msc:53D15

paper · pdf · doi:10.48550/arxiv.1805.08054

arXiv admin note: text overlap with arXiv:1804.02396, arXiv:1804.01599

arxiv created 2018/05/17 · arxiv updated 2018/05/28

Abstract

Let \widetildeJ be the canonical para-complex structure on ℝ²ⁿ⁺²≃\widetildeℂⁿ⁺¹. We study real affine hypersurfaces f\colon M→ \widetildeℂⁿ⁺¹ with a \widetildeJ-tangent transversal vector field. Such vector field induces in a natural way an almost paracontact structure (φ,ξ,η) on M as well as the affine connection ∇. In this paper we give the 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. Results we illustrate with some examples.

Citations

• On \widetildeJ-tangent affine hyperspheres

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