Bulletin of the Belgian Mathematical Society - Simon Stevin

Real hypersurfaces with Killing type structure Jacobi operators in $\mathbb{C}P^2$ and $\mathbb{C}H^2$

Yaning Wang and Wenjie Wang

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Abstract

In this paper, we prove that if the structure Jacobi operator of a $3$-dimen\-sional real hypersurface in a nonflat complex plane is of Killing type, then the hypersurface is either a tube of radius $\frac{\pi}{4}$ over a holomorphic curve in $\mathbb{C}P^2$ or a Hopf hypersurface with vanishing Hopf principal curvature in $\mathbb{C}H^2$. This extends the corresponding results in [6].

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 25, Number 3 (2018), 403-414.

Dates
First available in Project Euclid: 11 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1536631235

Digital Object Identifier
doi:10.36045/bbms/1536631235

Mathematical Reviews number (MathSciNet)
MR3852676

Zentralblatt MATH identifier
06970022

Subjects
Primary: 53B25: Local submanifolds [See also 53C40]
Secondary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.) 53D15: Almost contact and almost symplectic manifolds

Keywords
3-dimensional real hypersurface structure Jacobi operator Hopf hypersurface Killing tensor

Citation

Wang, Yaning; Wang, Wenjie. Real hypersurfaces with Killing type structure Jacobi operators in $\mathbb{C}P^2$ and $\mathbb{C}H^2$. Bull. Belg. Math. Soc. Simon Stevin 25 (2018), no. 3, 403--414. doi:10.36045/bbms/1536631235. https://projecteuclid.org/euclid.bbms/1536631235


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