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.
Henan Normal University
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).
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