Tsukuba Journal of Mathematics
- Tsukuba J. Math.
- Volume 42, Number 2 (2018), 127-154.
Commuting structure Jacobi operators for real hypersurfaces in complex space forms II
U-Hang Ki and Hiroyuki Kurihara
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
