Structure Jacobi Operators and Real Hypersurfaces of Type(A) in Complex Space Forms
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Let $M$ be a real hypersurface with almostcontact metric structure $(\phi, \xi, \eta, g)$ in a nonflat complex space form$M_n(c)$. We denote $S$ and $R_\xi$ by the Ricci tensor of $M$ and by the structureJacobi operator with respect to the vector field $\xi$ respectively. In this paper, we prove that $M$ is a Hopf hypersurface of type ($A$) in $M_n (c)$if it satisfies $R_\xi \phi=\phi R_\xi$ and at the same time satisfies $(\nabla_{\phi\nabla_{\xi}\xi} R_{\xi} )\xi=0$ or $R_\xi \phi S=S\phi R_\xi$.
Abstract
Let $M$ be a real hypersurface with almostcontact metric structure $(\phi, \xi, \eta, g)$ in a nonflat complex space form$M_n(c)$. We denote $S$ and $R_\xi$ by the Ricci tensor of $M$ and by the structureJacobi operator with respect to the vector field $\xi$ respectively. In this paper, we prove that $M$ is a Hopf hypersurface of type ($A$) in $M_n (c)$if it satisfies $R_\xi \phi=\phi R_\xi$ and at the same time satisfies $(\nabla_{\phi\nabla_{\xi}\xi} R_{\xi} )\xi=0$ or $R_\xi \phi S=S\phi R_\xi$.
참고문헌 (17)
- J. Berndt, "Real hypersurfaces with constant principal curvatures in a complex hyperbolic space", J. Reine Angew. Math, 395, pp.132~141 (1989)
- J. Berndt, "Cohomogeneity one actions on non compact symmetric spaces of rank one", Trans. Amer. Math. Soc, 359, pp.3425~3438 (2007)
- T. E. Cecil, "Focal sets and real hypersurfaces in complex projective space", Trans. Amer. Math. Soc, 269, pp.481~499 (1982)
- T. E. Cecil, "Geomytry of Hypersurrfaces" (2015), Springer
- J. T. Cho, "Real hypersurfaces of a complex projective space in terms of the Jacobi operators", Acta Math. Hungar, 80, pp.155~167 (1988)
- U-H. Ki, "Certain charaterization of real hypersurfaces of type A in a nonflat complex space form", Kyungpook Math. J
- 기우항, "CHARACTERIZATIONS OF REAL HYPERSURFACES OF TYPE A IN A COMPLEX SPACE FORM", 대한수학회보, 47(1), pp.1~15 (2010), 대한수학회
- 기우항, "The structure Jacobi Operator on real hypersurfaces in a nonflat complex space form", 대한수학회보, 42(2), pp.337~358 (2005), 대한수학회
- U-H. Ki, "Real hypersurfaces in nonflat complex forms conserned with the structure Jacobi operator and Ricci tensor, ”Topics in Almost Hermiwian Geometry and Related Field”", Proceed in honor of K.Sekigawa 60th birthday, World Scientific, pp.140~156 (2005)
- U-H. Ki, "Structure Jacobi operator of real hypersurfaces with constant scalar cuverture in a nonflat complex space form", Tokyo J. Math, 30, pp.441~454 (2007)
- U-H. Ki, "The sturcture vector field and structure Jacobi operator of real hypersurface in nonflat complex space forms", Geom. Dedicata, 149, pp.161~176 (2010)
- U-H. Ki, "On real hypersurfaces of a complex form", Math. J. Okayama Univ, 32, pp.207~221 (1990)
- I. -B. Kim, "On characterizations of Hopf hypersurfaces in a nonflat complex space form with commuting operators", Rocky Mountain. J. Math, 44, pp.1923~1939 (2014)
- S. Montiel, "On some real hypersurfaces of a complex hyperbolic space", Geom. Dedicata, 20, pp.45~261 (1986)
- M. Okumura, "On some real hypersurfaces of a complex projective space", Trans. Amer. Math. Soc, 212, pp.355~364 (1973)
- R. Takagi, "On homogeneous real hypersurfaces in a complex projective space", Osaka J. Math, 19, pp.495~506 (1973)
- R. Takagi, "Real hypersurfaces in a complex projective space with constant principal curvatures I,II", J. Math. Soc. Japan, 27, pp.43~53 (1975)