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

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...

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...

A certain tensor on real hypersurfaces in a nonflat complex space form

Kazuhiro Okumura (2020)

Czechoslovak Mathematical Journal

Similarity:

In a nonflat complex space form (namely, a complex projective space or a complex hyperbolic space), real hypersurfaces admit an almost contact metric structure $(φ, ξ, η, g)$ induced from the ambient space. As a matter of course, many geometers have investigated real hypersurfaces in a nonflat complex space form from the viewpoint of almost contact metric geometry. On the other hand, it is known that the tensor field $h$ $(= \frac{1}{2} ℒ_{ξ} φ)$ plays an important role in contact Riemannian geometry. In this...

Real hypersurfaces with parallel induced almost contact structures

Zuzanna Szancer (2012)

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 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

Similarity:

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

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 $E_{1}^{4}$ .

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