Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
권호 표지
DOI QR코드

DOI QR Code

Real Hypersurfaces in Complex Projective Space Whose Structure Jacobi Operator Is Cyclic-Ryan Parallel

  • Received : 2007.06.20
  • Accepted : 2007.09.30
  • Published : 2009.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

We classify real hypersurfaces in complex projective space whose structure Jacobi operator satisfies a certain cyclic condition.

Keywords

References

  1. Q. S. Chi, A curvature characterization of certain locally rank-one symmetric spaces, J. Diff. Geom., 28(1988), 187-202. https://doi.org/10.4310/jdg/1214442277
  2. J. T. Cho and U-H. Ki, Jacobi operators on real hypersurfaces of a complex projective space, Tsukuba J. Math., 22(1998), 145-156. https://doi.org/10.21099/tkbjm/1496163476
  3. J. T. Cho and U-H. Ki, Real hypersurfaces of a complex projective space in terms of the Jacobi operators, Acta Math. Hungar., 80(1998), 155-167. https://doi.org/10.1023/A:1006585128386
  4. U-H. Ki, H.J. Kim and A.A. Lee, The Jacobi operator of real hypersurfaces in a complex Space form, Commun. Korean Math. Soc., 13(1998), 545-600.
  5. M. Kimura, Sectional curvatures of holomorphic planes on a real hypersurface in $P^n(C)$, Math. Ann., 276(1987), 487-497. https://doi.org/10.1007/BF01450843
  6. M. Kimura and S. Maeda, On real hypersurfaces of a complex projective space III, Hokkaido Math. J., 22(1993), 63-78. https://doi.org/10.14492/hokmj/1381413124
  7. M. Loknherr and H. Reckziegel, On ruled real hypersurfaces in complex space forms, Geom. Dedicata, 74(1999), 267-286. https://doi.org/10.1023/A:1005000122427
  8. M. Okumura, On some real hypersurfaces of a c omplex projective space, Trans. A. M. S., 212(1975), 355-364. https://doi.org/10.1090/S0002-9947-1975-0377787-X
  9. M. Ortega, J. D. Perez and F. G. Santos, Non-existence of real hypersurfaces with parallel structure Jacobi operator in nonflat complex space forms, Rocky Mountain J. Math., 36(2006), 1603-1613. https://doi.org/10.1216/rmjm/1181069385
  10. J. D. Perez and F. G. Santos, On the Lie derivative of structure Jacobi operator of real hypersurfaces in complex projective space, Publ. Math. Debrecen, 66(2005), 269-282.
  11. J. D. Perez and F. G. Santos, Real hypersurfaces in complex projective space with recurrent structure Jacobi operator, Diff. Geom. Appl., 26(2008), 218-223. https://doi.org/10.1016/j.difgeo.2007.11.015
  12. J. D. Perez, F. G. Santos and Y. J. Suh, Real hypersurfaces in complex projective space whose structure Jacobi operator is Lie $\varepsilon$-parallel, Diff. Geom. Appl., 22(2005),181-188. https://doi.org/10.1016/j.difgeo.2004.10.005
  13. J. D. Perez, F. G. Santos and Y. J. Suh, Real hypersurfaces in complex projective space whose structure Jacobi operator is D-parallel, Bull. Belgian Math. Soc. Simon Stevin, 13(2006), 459-469.
  14. R. Takagi, On homogeneous real hypersurfaces in a complex projective space, Osaka J. Math., 10(1973), 495-506.
  15. R. Takagi, Real hypersurfaces in complex projective space with constant principal curvatures, J. Math. Soc. Japan, 27(1975), 43-53. https://doi.org/10.2969/jmsj/02710043
  16. R. Takagi, Real hypersurfaces in complex projective space with constant principal curvatures II, J. Math. Soc. Japan, 27(1975), 507-516. https://doi.org/10.2969/jmsj/02740507

Cited by

  1. Semi-parallelism of normal Jacobi operator for Hopf hypersurfaces in complex two-plane Grassmannians vol.172, pp.2, 2013, https://doi.org/10.1007/s00605-013-0553-7
  2. Semi-parallel symmetric operators for Hopf hypersurfaces in complex two-plane Grassmannians vol.177, pp.4, 2015, https://doi.org/10.1007/s00605-015-0778-8