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Real hypersurfaces with parallel induced almost contact structures

100%
Szancer Z.
Annales Polonici Mathematici
|
2012
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tom 104
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nr 2
203-215
EN
Real affine hypersurfaces of the complex space $ℂ^{n+1}$ with a J-tangent transversal vector field and an induced almost contact structure (φ,ξ,η) are studied. Some properties of hypersurfaces with φ or η parallel relative to an induced connection are proved. Also a local characterization of these hypersurfaces is given.
2
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Real hypersurfaces with a special transversal vector field

100%
Szancer Z.
Annales Polonici Mathematici
|
2012
|
tom 105
|
nr 3
239-252
EN
Real affine hypersurfaces of the complex space $ℂ^{n+1}$ are studied. Some properties of the structure determined by a J-tangent transversal vector field are proved. Moreover, some generalizations of the results obtained by V. Cruceanu are given.
3
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On some properties of induced almost contact structures

100%
Szancer Z.
Annales Polonici Mathematici
|
2015
|
tom 113
|
nr 1
81-92
EN
Real affine hypersurfaces of the complex space $ℂ^{n+1}$ with a J-tangent transversal vector field and an induced almost contact structure (φ,ξ,η) are studied. Some properties of the induced almost contact structures are proved. In particular, we prove some properties of the induced structure when the distribution 𝓓 is involutive. Some constraints on a shape operator when the induced almost contact structure is either normal or ξ-invariant are also given.
4
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Real hypersurfaces with an induced almost contact structure

63%
Szancer M., Szancer Z.
Colloquium Mathematicum
|
2009
|
tom 114
|
nr 1
41-51
EN
We study real affine hypersurfaces $f: M → ℂ^{n+1}$ with an almost contact structure (φ,ξ,η) induced by any J-tangent transversal vector field. The main purpose of this paper is to show that if (φ,ξ,η) is metric relative to the second fundamental form then it is Sasakian and moreover f(M) is a piece of a hyperquadric in $ℝ^{2n+2}$.
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