Tsukuba Journal of Mathematics

Jacobi operators on real hypersurfaces of a complex projective space

Jong Taek Cho and U-Hang Ki

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In this paper, we investigate a real hypersurface of a complex projective space $CP^{n}$ in terms of the Jacobi operators. We give a local stmcture theorem of a real hypersurface of $CP^{n}$ satisisfying $R_{\xi}=k(I-\eta\otimes\xi)$, where $ R_{\xi}=R(\cdot, \xi)\xi$ the Jacobi operator with respect to $\xi$ and $k$ is a function. Further, we classify real hypersurfaces of $CP^{n}$ satisfying $\phi R_{\xi}=R_{\xi}\phi$ under the condition that $ A\xi$ is a principal curvature vector. Also, we show that a complex projective space does not admit a locally symmetric real hypersurface.

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Tsukuba J. Math., Volume 22, Number 1 (1998), 145-156.

First available in Project Euclid: 30 May 2017

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Cho, Jong Taek; Ki, U-Hang. Jacobi operators on real hypersurfaces of a complex projective space. Tsukuba J. Math. 22 (1998), no. 1, 145--156. doi:10.21099/tkbjm/1496163476. https://projecteuclid.org/euclid.tkbjm/1496163476

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