Tsukuba Journal of Mathematics

Commuting structure Jacobi operators for real hypersurfaces in complex space forms II

U-Hang Ki and Hiroyuki Kurihara

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Abstract

Let $M$ be a real hypersurface in a complex space form $M_n(c)$, $c \not= 0$. In this paper, we prove that if the structure Jacobi operator $R_\xi$ is $\phi\nabla_{\xi}\xi$-parallel and $R_\xi$ commute with the Ricci tensor, then $M$ is a Hopf hypersurface provided that the mean curvature of $M$ is constant with respect to the structure vector field.

Article information

Source
Tsukuba J. Math., Volume 42, Number 2 (2018), 127-154.

Dates
First available in Project Euclid: 2 April 2019

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1554170419

Digital Object Identifier
doi:10.21099/tkbjm/1554170419

Mathematical Reviews number (MathSciNet)
MR3934985

Zentralblatt MATH identifier
07055227

Subjects
Primary: 53B20: Local Riemannian geometry 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)

Keywords
complex space form real hypersurface structure Jacobi operator Hopf hypersurfaces Ricci tensor mean curvature

Citation

Ki, U-Hang; Kurihara, Hiroyuki. Commuting structure Jacobi operators for real hypersurfaces in complex space forms II. Tsukuba J. Math. 42 (2018), no. 2, 127--154. doi:10.21099/tkbjm/1554170419. https://projecteuclid.org/euclid.tkbjm/1554170419


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