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

Hyunjin Lee; Seonhui Kim; Young Jin Suh

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

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

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

Czechoslovak Mathematical Journal

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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...

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 in complex space forms concerned with the local symmetry

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

Czechoslovak Mathematical Journal

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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.

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 $M$ .

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.

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.

Real hypersurfaces in complex two-plane Grassmannians with recurrent shape operator.

Kim, Seonhui, Lee, Hyunjin, Yang, Hae Young (2011)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

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