Kyungpook Mathematical Journal

  • 제56권3호
  • /
  • Pages.993-1002
  • /
  • 2016
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  • 1225-6951(pISSN)
  • /
  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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Characterizations for Real Hypersurfaces in Complex and Quaternionic Space Forms Related to the Normal Jacobi Operator

  • Jeong, Imsoon (Department of Mathematics, Kyungpook National University) ;
  • Kim, Gyu Jong (Department of Mathematics, Kyungpook National University) ;
  • Kim, Kyoung Nam (Department of Mathematics, Kyungpook National University)
  • 투고 : 2015.11.13
  • 심사 : 2016.05.11
  • 발행 : 2016.09.23
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초록

In this paper we give some non-existence theorems for parallel normal Jacobi operator of real hypersurfaces in real, complex and quaternionic space forms, respectively.

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참고문헌

  1. J. Berndt, Real hypersurfaces in quaternionic space forms, J. Reine Angew. Math., 419(1991), 9-26.
  2. J. Berndt and Y. J. Suh, Real hypersurfaces in complex two-plane Grassmannians, Monatsh. Math., 127(1999), 1-14. https://doi.org/10.1007/s006050050018
  3. D. H. Hwang, H. Lee and C. Woo, Semi-parallel symmetirc operators for Hopf hypersurfaces in complex two-plane Grassmannians, Monatsh. Math., 177(4)(2015), 539-550. https://doi.org/10.1007/s00605-015-0778-8
  4. I. Jeong, H. J. Kim and Y. J. Suh, Real hypersurfaces in complex two-plane Grass- mannians with parallel normal Jacobi operator, Publ. Math. Debrecen, 76(2010), no. 1-2, 203-218.
  5. I. Jeong and Y. J. Suh, Real hypersurfaces in complex two-plane Grassmannians with F-parallel normal Jacobi operator, Kyungpook Math. J., 51(2011), no. 4, 395-410. https://doi.org/10.5666/KMJ.2011.51.4.395
  6. M. Kimura, Sectional curvatures of holomorphic planes on a real hypersurface in PnC, Math. Ann., 276(1987), 487-499. https://doi.org/10.1007/BF01450843
  7. C. J. G. Machado, J. D. Perez, I. Jeong and Y. J. Suh, Real hypersurfaces in complex two-plane Grassmannians whose normal Jacobi operator is of Codazzi type, Cent. Eur. J. Math., 9(3)(2011), 578-582. https://doi.org/10.2478/s11533-011-0022-2
  8. C. J. G. Machado, J. D. Perez, I. Jeong and Y. J. Suh, D-parallelism of normal and structure Jacobi operators for hypersurfaces in complex two-plane Grassmannians, Ann. Mat. Pura Appl., 193(2014), 591-608. https://doi.org/10.1007/s10231-012-0292-8
  9. M. Ortega and J. D. Perez, Real hypersurfaces with constant totally real sectional curvatures in complex space form, Czechoslovak Math. J., 50(2000), 531-537. https://doi.org/10.1023/A:1022881510000
  10. K. Panagiotidou and M. M. Tripathi, Semi-parallelism of normal Jacobi opera- tor for Hopf hypersurfaces in complex two-plane Grassmannians, Monatsh. Math., 172(2)(2013), 167-178. https://doi.org/10.1007/s00605-013-0553-7
  11. J. D. Perez and Y. J. Suh, Real hypersurfaces of quaternionic projecitve space satis- fying ${\nabla}_{Ui}R=0$, Differential Geom. Appl., 7(1997), 211-217. https://doi.org/10.1016/S0926-2245(97)00003-X
  12. D. J. Sohn and Y. J. Suh, Classi cation of real hypersurfaces in complex hyperbolic space in terms of constant $\phi$-holomorphic sectional curvatures, Kyungpook Math. J., 35(1996), 801-819.
  13. Y. J. Suh, A characterization of ruled real hypersurfaces in PnC, J. Korean Math. Soc., 29(1992), 351-359.