Some characterizations of ruled real hypersurfaces in a complex space form

U Hang Ki; Young Jin Suh

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 1996; 33(1): 101-119

Printed March 1, 1996

Some characterizations of ruled real hypersurfaces in a complex space form

U Hang Ki and Young Jin Suh

Kyungpook National University and Kyungpook National University

Abstract

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Abstract

In this paper firstly we give the notion of ruled real hypersurfaces in a non-flat complex space form $M_n(c)$ and calculate the expression of the covariant derivative $({\nabla}_XA)Y$ of its Weingarten map $A$ for $X$,$Y$ in a distribution $T_0$. Next we consider the $\xi$-component $g(({\nabla}_XA)Y,{\xi}) =f(X,Y),\ X,Y$ in $T_0$, with which we study a characterization of ruled real hypersurfaces in $M_n(c)$. As an application of this characterization we can also obtain another characterization of these hypersurfaces in terms of Lie derivatives.

Keywords: $T_0$-component, $\xi$-component, ruled real hypersurfaces

MSC numbers: Primary 53C40; Secondary 53C15