# A characterization of a certain real hypersurface of type $\left({\mathrm{A}}_{2}\right)$ in a complex projective space

Byung Hak Kim; In-Bae Kim; Sadahiro Maeda

Czechoslovak Mathematical Journal (2017)

- Volume: 67, Issue: 1, page 271-278
- ISSN: 0011-4642

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topKim, Byung Hak, Kim, In-Bae, and Maeda, Sadahiro. "A characterization of a certain real hypersurface of type $({\rm A}_2)$ in a complex projective space." Czechoslovak Mathematical Journal 67.1 (2017): 271-278. <http://eudml.org/doc/287912>.

@article{Kim2017,

abstract = {In the class of real hypersurfaces $M^\{2n-1\}$ isometrically immersed into a nonflat complex space form $\widetilde\{M\}_n(c)$ of constant holomorphic sectional curvature $c$$(\ne 0)$ which is either a complex projective space $\mathbb \{C\}P^n(c)$ or a complex hyperbolic space $\mathbb \{C\}H^n(c)$ according as $c > 0$ or $c < 0$, there are two typical examples. One is the class of all real hypersurfaces of type (A) and the other is the class of all ruled real hypersurfaces. Note that the former example are Hopf manifolds and the latter are non-Hopf manifolds. In this paper, inspired by a simple characterization of all ruled real hypersurfaces in $\widetilde\{M\}_n(c)$, we consider a certain real hypersurface of type $(\{\rm A\}_2)$ in $\mathbb \{C\}P^n(c)$ and give a geometric characterization of this Hopf manifold.},

author = {Kim, Byung Hak, Kim, In-Bae, Maeda, Sadahiro},

journal = {Czechoslovak Mathematical Journal},

keywords = {ruled real hypersurface; nonflat complex space form; real hypersurfaces of type $(\{\rm A\}_2)$ in a complex projective space; geodesics; structure torsion; Hopf manifold},

language = {eng},

number = {1},

pages = {271-278},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {A characterization of a certain real hypersurface of type $(\{\rm A\}_2)$ in a complex projective space},

url = {http://eudml.org/doc/287912},

volume = {67},

year = {2017},

}

TY - JOUR

AU - Kim, Byung Hak

AU - Kim, In-Bae

AU - Maeda, Sadahiro

TI - A characterization of a certain real hypersurface of type $({\rm A}_2)$ in a complex projective space

JO - Czechoslovak Mathematical Journal

PY - 2017

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 67

IS - 1

SP - 271

EP - 278

AB - In the class of real hypersurfaces $M^{2n-1}$ isometrically immersed into a nonflat complex space form $\widetilde{M}_n(c)$ of constant holomorphic sectional curvature $c$$(\ne 0)$ which is either a complex projective space $\mathbb {C}P^n(c)$ or a complex hyperbolic space $\mathbb {C}H^n(c)$ according as $c > 0$ or $c < 0$, there are two typical examples. One is the class of all real hypersurfaces of type (A) and the other is the class of all ruled real hypersurfaces. Note that the former example are Hopf manifolds and the latter are non-Hopf manifolds. In this paper, inspired by a simple characterization of all ruled real hypersurfaces in $\widetilde{M}_n(c)$, we consider a certain real hypersurface of type $({\rm A}_2)$ in $\mathbb {C}P^n(c)$ and give a geometric characterization of this Hopf manifold.

LA - eng

KW - ruled real hypersurface; nonflat complex space form; real hypersurfaces of type $({\rm A}_2)$ in a complex projective space; geodesics; structure torsion; Hopf manifold

UR - http://eudml.org/doc/287912

ER -

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