Rocky Mountain Journal of Mathematics

On characterizations of Hopf hypersurfaces in a nonflat complex space form with commuting operators

In-Bae Kim, Dong Ho Lim, and Hyunjung Song

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Abstract

Let $M$ be a real hypersurface in a complex space form $\mn$, $c \neq 0$. In this paper we prove that if $\rx\li = \li\rx$ holds on $M$, then $M$ is a Hopf hypersurface, where $\rx$ and $\li$ denote the structure Jacobi operator and the induced operator from the Lie derivative with respect to the structure vector field $\xi$, respectively. We characterize such Hopf hypersurfaces of $\mn$.

Article information

Source
Rocky Mountain J. Math., Volume 44, Number 6 (2014), 1923-1939.

Dates
First available in Project Euclid: 2 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1422885101

Digital Object Identifier
doi:10.1216/RMJ-2014-44-6-1923

Mathematical Reviews number (MathSciNet)
MR3310955

Zentralblatt MATH identifier
1315.53057

Subjects
Primary: 53C40: Global submanifolds [See also 53B25]
Secondary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)

Keywords
Real hypersurface structure Jacobi operator Hopf hypersurface model spaces of type A

Citation

Kim, In-Bae; Lim, Dong Ho; Song, Hyunjung. On characterizations of Hopf hypersurfaces in a nonflat complex space form with commuting operators. Rocky Mountain J. Math. 44 (2014), no. 6, 1923--1939. doi:10.1216/RMJ-2014-44-6-1923. https://projecteuclid.org/euclid.rmjm/1422885101


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