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

Title:

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

Creator:

Kon, Mayuko

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:700d08be-e0a6-435b-b72a-8264abc3fcc2
uuid:700d08be-e0a6-435b-b72a-8264abc3fcc2

Subject:

real hypersurface, totally $\eta $-umbilical real hypersurface, and ruled real hypersurface

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We give a characterization of totally $\eta $-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 $g(AX,Y)=ag(X,Y)$ 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 $\eta $-umbilical real hypersurface or locally congruent to a ruled real hypersurface. This condition for the shape operator is a generalization of the notion of $\eta $-umbilical real hypersurfaces.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

1279-1287

Source:

Czechoslovak Mathematical Journal | 2008 Volume:58 | Number:4

Harvested from:

CDK

Metadata only:

false