Parallel almost paracontact structures on affine hypersurfaces
AbstractLet 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.
|Journal series||Annales Polonici Mathematici, ISSN 0066-2216, e-ISSN 1730-6272, (N/A 70 pkt)|
|Publication size in sheets||0.8|
|Publication indicators||= 0; : 2018 = 0.506; : 2018 = 0.5 (2) - 2018=0.463 (5)|
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