Tokyo Journal of Mathematics

Structure Jacobi Operator of Real Hypersurfaces with Constant Scalar Curvature in a Nonflat Complex Space Form

U-Hang KI, Setsuo NAGAI, and Ryoichi TAKAGI

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Abstract

Let $M$ be a real hypersurface with almost contact metric structure $(\phi ,\xi ,\eta ,g)$ in a nonflat complex space form $M_{n}(c)$. We denote by $S$ be the Ricci tensor of $M$. In the present paper we investigate real hypersurfaces with constant scalar curvature of $M_{n}(c)$ whose structure Jacobi operator $R_{\xi}$ commute with both $\phi$ and $S$. We characterize Hopf hypersurfaces of $M_{n}(c)$.

Article information

Source
Tokyo J. Math., Volume 30, Number 2 (2007), 441-454.

Dates
First available in Project Euclid: 4 February 2008

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1202136687

Digital Object Identifier
doi:10.3836/tjm/1202136687

Mathematical Reviews number (MathSciNet)
MR2376520

Zentralblatt MATH identifier
1145.53043

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

Citation

KI, U-Hang; NAGAI, Setsuo; TAKAGI, Ryoichi. Structure Jacobi Operator of Real Hypersurfaces with Constant Scalar Curvature in a Nonflat Complex Space Form. Tokyo J. Math. 30 (2007), no. 2, 441--454. doi:10.3836/tjm/1202136687. https://projecteuclid.org/euclid.tjm/1202136687


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