Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2022; 59(4): 897-904

Published online July 31, 2022 https://doi.org/10.4134/BKMS.b210514

Copyright © The Korean Mathematical Society.

A new characterization of type $(A)$ and ruled real hypersurfaces in nonflat complex space forms

Yaning Wang

Henan Normal University

Abstract

In this paper, we obtain an inequality involving the squared norm of the covariant differentiation of the shape operator for a real hypersurface in nonflat complex space forms. It is proved that the equality holds for non-Hopf case if and only if the hypersurface is ruled and the equality holds for Hopf case if and only if the hypersurface is of type $(A)$.

Keywords: Ruled real hypersurface, nonflat complex space, shape operator, norm

MSC numbers: Primary 53C25, 53D10

Supported by: This work was supported by the Key Scientific Research Program in Universities of Henan Province (No. 20A110023) and the Fostering Foundation of National Foundation in Henan Normal University (No. 2019PL22).