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

Mayuko Kon

Displaying similar documents to “A characterization of totally $η$ -umbilical real hypersurfaces and ruled real hypersurfaces of a complex space form”

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...

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 in complex two-plane Grassmannians with certain commuting condition

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

Czechoslovak Mathematical Journal

Similarity:

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...

Displaying similar documents to “A characterization of totally η -umbilical real hypersurfaces and ruled real hypersurfaces of a complex space form”

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

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

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

Displaying similar documents to “A characterization of totally $η$ -umbilical real hypersurfaces and ruled real hypersurfaces of a complex space form”