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http://dx.doi.org/10.4134/BKMS.2005.42.2.337

THE STRUCTURE JACOBI OPERATOR ON REAL HYPERSURFACES IN A NONFLAT COMPLEX SPACE FORM  

KI, U-HANG (DEPARTMENT OF MATHEMATICS, KYUNGPOOK NATIONAL UNIVERSITY)
KIM, SOO-JIN (DEPARTMENT OF MATHEMATICS, CHOSUN UNIVERSITY)
LEE, SEONG-BAEK (DEPARTMENT OF MATHEMATICS, CHOSUN UNIVERSITY)
Publication Information
Bulletin of the Korean Mathematical Society / v.42, no.2, 2005 , pp. 337-358 More about this Journal
Abstract
Let M be a real hypersurface with almost contact metric structure $(\phi,\;\xi,\;\eta,\;g)$ in a nonflat complex space form $M_n(c)$. In this paper, we prove that if the structure Jacobi operator $R_\xi$ commutes with both the structure tensor $\phi$ and the Ricc tensor S, then M is a Hopf hypersurface in $M_n(c)$ provided that the mean curvature of M is constant or $g(S\xi,\;\xi)$ is constant.
Keywords
structure Jacobi operator; Ricci tensor; Hopf hypersurface; nonflat complex space form;
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