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

Hyunjin Lee; Seonhui Kim; Young Jin Suh

Displaying similar documents to “Real hypersurfaces in complex two-plane Grassmannians with certain commuting condition II”

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

Hyunjin Lee, Seonhui Kim, Young Jin Suh (2012)

Czechoslovak Mathematical Journal

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In this paper, first we introduce a new notion of commuting condition that $φ φ_{1} A = A φ_{1} φ$ between the shape operator $A$ and the structure tensors $φ$ and $φ_{1}$ for real hypersurfaces in $G_{2} (ℂ^{m + 2})$ . Suprisingly, real hypersurfaces of type $(A)$ , that is, a tube over a totally geodesic $G_{2} (ℂ^{m + 1})$ in complex two plane Grassmannians $G_{2} (ℂ^{m + 2})$ satisfy this commuting condition. Next we consider a complete classification of Hopf hypersurfaces in $G_{2} (ℂ^{m + 2})$ satisfying the commuting condition. Finally we get a characterization of Type $(A)$ in terms of such...

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

Mayuko Kon (2008)

Czechoslovak Mathematical Journal

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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...

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.

Geometry of holomorphic distributions of real hypersurfaces in a complex projective space

U-Hang Ki, Makoto Kimura, Sadahiro Maeda (2001)

Czechoslovak Mathematical Journal

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We characterize homogeneous real hypersurfaces $M$ ’s of type $(A_{1})$ , $(A_{2})$ and $(B)$ of a complex projective space in the class of real hypersurfaces by studying the holomorphic distribution $T^{0} M$ of $M$ .

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

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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 $E_{1}^{4}$ .

Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster parallel normal Jacobi operator

Eunmi Pak, Juan de Dios Pérez, Carlos J. G. Machado, Changhwa Woo (2015)

Czechoslovak Mathematical Journal

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We study the classifying problem of immersed submanifolds in Hermitian symmetric spaces. Typically in this paper, we deal with real hypersurfaces in a complex two-plane Grassmannian $G_{2} (ℂ^{m + 2})$ which has a remarkable geometric structure as a Hermitian symmetric space of rank 2. In relation to the generalized Tanaka-Webster connection, we consider a new concept of the parallel normal Jacobi operator for real hypersurfaces in $G_{2} (ℂ^{m + 2})$ and prove non-existence of real hypersurfaces in $G_{2} (ℂ^{m + 2})$ with generalized...

Examples of nonsemisymmetric Ricci-semisymmetric hypersurfaces

Ryszard Deszcz, Malgorzata Głogowska (2002)

Colloquium Mathematicae

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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.

Generalized Tanaka-Webster and Levi-Civita connections for normal Jacobi operator in complex two-plane Grassmannians

Eunmi Pak, Juan de Dios Pérez, Young Jin Suh (2015)

Czechoslovak Mathematical Journal

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We study classifying problems of real hypersurfaces in a complex two-plane Grassmannian $G_{2} (ℂ^{m + 2})$ . In relation to the generalized Tanaka-Webster connection, we consider that the generalized Tanaka-Webster derivative of the normal Jacobi operator coincides with the covariant derivative. In this case, we prove complete classifications for real hypersurfaces in $G_{2} (ℂ^{m + 2})$ satisfying such conditions.

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 $ℝ^{2 n + 2}$ .