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Korean Mathematical Society BKMS

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Bull. Korean Math. Soc. 2007; 44(1): 195-202

Printed March 1, 2007

Copyright © The Korean Mathematical Society.

Characterizations of real hypersurfaces of complex space forms in terms of Ricci operators

Woon Ha Sohn

Hankuk University of Foreign Studies

Abstract

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We prove that a real hypersurface $M$ in a complex space form $M_n(c)$, $c \neq 0$, whose Ricci operator and structure tensor commute each other on the holomorphic distribution and the Ricci operator is $\eta$-parallel, is a Hopf hypersurface. We also give a characterization of this hypersurface.

Keywords: real hypersurfaces in complex space forms, Hopf hypersurfaces, model spaces of type A or B

MSC numbers: Primary 53C40; Secondary 53C15

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