Real hypersurfaces with parallel induced almost contact structures

Zuzanna Szancer

Displaying similar documents to “Real hypersurfaces with parallel induced almost contact structures”

Real hypersurfaces with a special transversal vector field

Zuzanna Szancer (2012)

Annales Polonici Mathematici

Similarity:

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.

Real hypersurfaces with an induced almost contact structure

Michał Szancer, Zuzanna Szancer (2009)

Colloquium Mathematicae

Similarity:

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 $ℝ^{2 n + 2}$ .

On some properties of induced almost contact structures

Zuzanna Szancer (2015)

Annales Polonici Mathematici

Similarity:

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.

Bernstein type properties of two-sided hypersurfaces immersed in a Killing warped product

Antonio W. Cunha, Eudes L. de Lima, Henrique F. de Lima, Eraldo A. Lima Jr., Adriano A. Medeiros (2016)

Studia Mathematica

Similarity:

Our purpose is to apply suitable maximum principles in order to obtain Bernstein type properties for two-sided hypersurfaces immersed with constant mean curvature in a Killing warped product $M ⁿ \times_{ρ} ℝ$ , whose curvature of the base Mⁿ satisfies certain constraints and whose warping function ρ is concave on Mⁿ. For this, we study situations in which these hypersurfaces are supposed to be either parabolic, stochastically complete or, in a more general setting, L¹-Liouville. Rigidity results related...

A characterization of totally $η$ -umbilical real hypersurfaces and ruled real hypersurfaces of a complex space form

Mayuko Kon (2008)

Czechoslovak Mathematical Journal

Similarity:

We give a characterization of totally $η$ -umbilical real hypersurfaces and ruled real hypersurfaces of a complex space form in terms of totally umbilical condition for the holomorphic distribution on real hypersurfaces. We prove that if the shape operator $A$ of a real hypersurface $M$ of a complex space form $M^{n} (c)$ , $c \neq 0$ , $n \geq 3$ , satisfies $g (A X, Y) = a g (X, Y)$ for any $X, Y \in T_{0} (x)$ , $a$ being a function, where $T_{0}$ is the holomorphic distribution on $M$ , then $M$ is a totally $η$ -umbilical real hypersurface or locally congruent to a ruled real...

Parallel hypersurfaces

Barbara Opozda, Udo Simon (2014)

Annales Polonici Mathematici

Similarity:

We investigate parallel hypersurfaces in the context of relative hypersurface geometry, in particular including the cases of Euclidean and Blaschke hypersurfaces. We describe the geometric relations between parallel hypersurfaces in terms of deformation operators, and we apply the results to the parallel deformation of special classes of hypersurfaces, e.g. quadrics and Weingarten hypersurfaces.

A class of complex hypersurfaces

Patrick J. Ryan (1972)

Colloquium Mathematicae

Similarity:

Non-existence of real lightlike hypersurfaces of an indefinite complex space form.

Ṣahin, Bayram, Güneṣ, Rifat (2000)

Balkan Journal of Geometry and its Applications (BJGA)

Similarity:

Real hypersurfaces in complex two-plane Grassmannians with certain commuting condition II

Hyunjin Lee, Seonhui Kim, Young Jin Suh (2014)

Czechoslovak Mathematical Journal

Similarity:

Lee, Kim and Suh (2012) gave a characterization for real hypersurfaces $M$ of Type $(A)$ in complex two plane Grassmannians $G_{2} (ℂ^{m + 2})$ with a commuting condition between the shape operator $A$ and the structure tensors $φ$ and $φ_{1}$ for $M$ in $G_{2} (ℂ^{m + 2})$ . Motivated by this geometrical notion, in this paper we consider a new commuting condition in relation to the shape operator $A$ and a new operator $φ φ_{1}$ induced by two structure tensors $φ$ and $φ_{1}$ . That is, this commuting shape operator is given by $φ φ_{1} A = A φ φ_{1}$ . Using this condition, we...

Real hypersurfaces in complex space forms concerned with the local symmetry

Seon Mi Lyu, Juan de Dios Pérez, Young Jin Suh (2007)

Czechoslovak Mathematical Journal

Similarity:

This paper consists of two parts. In the first, we find some geometric conditions derived from the local symmetry of the inverse image by the Hopf fibration of a real hypersurface $M$ in complex space form $M_{m} (4 ϵ)$ . In the second, we give a complete classification of real hypersurfaces in $M_{m} (4 ϵ)$ which satisfy the above geometric facts.

Spacelike intersection curve of three spacelike hypersurfaces in $E_{1}^{4}$

B. Uyar Duldul, M. Caliskan (2013)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

Similarity:

In this paper, we compute the Frenet vectors and the curvatures of the spacelike intersection curve of three spacelike hypersurfaces given by their parametric equations in four-dimensional Minkowski space $E_{1}^{4}$ .

Isoparametric hypersurfaces with less than four principal curvatures in a sphere

Toshiaki Adachi, Sadahiro Maeda (2006)

Colloquium Mathematicae

Similarity:

We characterize Clifford hypersurfaces and Cartan minimal hypersurfaces in a sphere by some properties of extrinsic shapes of their geodesics.

Examples of nonsemisymmetric Ricci-semisymmetric hypersurfaces

Ryszard Deszcz, Malgorzata Głogowska (2002)

Colloquium Mathematicae

Similarity:

We construct a class of nonsemisymmetric Ricci-semisymmetric warped products. Some manifolds of this class can be locally realized as hypersurfaces of a semi-Euclidean space $_{s}^{n + 1}$ , n ≥ 5.

Integral formulas for closed spacelike hypersurfaces in anti-de Sitter space $H_{1}^{n + 1} (- 1)$

Guoxin Wei, Qiuli Liu, Young Jin Suh (2009)

Czechoslovak Mathematical Journal

Similarity:

In this paper, we study closed $k$ -maximal spacelike hypersurfaces $M^{n}$ in anti-de Sitter space $H_{1}^{n + 1} (- 1)$ with two distinct principal curvatures and give some integral formulas about these hypersurfaces.