Hypersurfaces with almost complex structures in the real affine space

Mayuko Kon

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Displaying similar documents to “Hypersurfaces with almost complex structures in the real affine space”

Real hypersurfaces with a special transversal vector field

Zuzanna Szancer (2012)

Annales Polonici Mathematici

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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.

A Remark on a Paper of Crachiola and Makar-Limanov

Robert Dryło (2011)

Bulletin of the Polish Academy of Sciences. Mathematics

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A. Crachiola and L. Makar-Limanov [J. Algebra 284 (2005)] showed the following: if X is an affine curve which is not isomorphic to the affine line $¹_{k}$ , then ML(X×Y) = k[X]⊗ ML(Y) for every affine variety Y, where k is an algebraically closed field. In this note we give a simple geometric proof of a more general fact that this property holds for every affine variety X whose set of regular points is not k-uniruled.

A local characterization of affine holomorphic immersions with an anti-complex and ∇-parallel shape operator

Maria Robaszewska (2002)

Annales Polonici Mathematici

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We study the complex hypersurfaces $f : M^{(n)} \to ℂ^{n + 1}$ which together with their transversal bundles have the property that around any point of M there exists a local section of the transversal bundle inducing a ∇-parallel anti-complex shape operator S. We give a class of examples of such hypersurfaces with an arbitrary rank of S from 1 to [n/2] and show that every such hypersurface with positive type number and S ≠ 0 is locally of this kind, modulo an affine isomorphism of $ℂ^{n + 1}$ .

On some properties of induced almost contact structures

Zuzanna Szancer (2015)

Annales Polonici Mathematici

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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 is involutive. Some constraints on a shape operator when the induced almost contact structure is either normal or ξ-invariant are also given.

Affine higher order parallel hypersurfaces

Luc Vrancken (1988)

Annales de la Faculté des sciences de Toulouse : Mathématiques

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Real hypersurfaces with an induced almost contact structure

Michał Szancer, Zuzanna Szancer (2009)

Colloquium Mathematicae

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We study real affine hypersurfaces $f : M \to ℂ^{n + 1}$ 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 $ℝ^{2 n + 2}$ .

General-affine invariants of plane curves and space curves

Shimpei Kobayashi, Takeshi Sasaki (2020)

Czechoslovak Mathematical Journal

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We present a fundamental theory of curves in the affine plane and the affine space, equipped with the general-affine groups $GA (2) = GL (2, ℝ) ⋉ ℝ^{2}$ and $GA (3) = GL (3, ℝ) ⋉ ℝ^{3}$ , respectively. We define general-affine length parameter and curvatures and show how such invariants determine the curve up to general-affine motions. We then study the extremal problem of the general-affine length functional and derive a variational formula. We give several examples of curves and also discuss some relations with equiaffine treatment and...

Affine isoparametric hypersurfaces.

R. Niebergall, P.J. Ryan (1994)

Mathematische Zeitschrift

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Special Kaehler manifolds: A survey

Cortés, Vincente

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This is a survey of recent contributions to the area of special Kähler geometry. A (pseudo-)Kähler manifold $(M, J, g)$ is a differentiable manifold endowed with a complex structure $J$ and a (pseudo-)Riemannian metric $g$ such that i) $J$ is orthogonal with respect to the metric $g,$ ii) $J$ is parallel with respect to the Levi Civita connection $D .$ A special Kähler manifold $(M, J, g, \nabla)$ is a Kähler manifold $(M, J, g)$ together with a flat torsionfree connection $\nabla$ such that i) $\nabla ω = 0,$ where $ω = g (., J .)$ is the Kähler form and ii) $\nabla$ is symmetric....

An Obstruction to the Existence of Affine Structures.

John Smillie (1981)

Inventiones mathematicae

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Real hypersurfaces with parallel induced almost contact structures

Zuzanna Szancer (2012)

Annales Polonici Mathematici

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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.

Closed parallel 1-forms on infranilmanifolds and Calabi reductions

Michał Sadowski (1990)

Colloquium Mathematicae

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Dual Connections and Affine Geometry.

Takashi Kurose (1990)

Mathematische Zeitschrift

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Affine Dunkl processes of type ${\tilde{A}}_{1}$

François Chapon (2012)

Annales de l'I.H.P. Probabilités et statistiques

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We introduce the analogue of Dunkl processes in the case of an affine root system of type ${\tilde{A}}_{1}$ . The construction of the affine Dunkl process is achieved by a skew-product decomposition by means of its radial part and a jump process on the affine Weyl group, where the radial part of the affine Dunkl process is given by a Gaussian process on the ultraspherical hypergroup $[0, 1]$ . We prove that the affine Dunkl process is a càdlàg Markov process as well as a local martingale, study its jumps, and...