Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

PSEUDO-PARALLEL REAL HYPERSURFACES IN COMPLEX SPACE FORMS

  • Lobos, Guillermo A. (Departmento de Matematica, Universidade Federalde Sao Carlos) ;
  • Ortega, Miguel (Departmento de Geometria Y Topologia, Facultad de Ciencias, Universidad De Granada)
  • Published : 2004.11.01
Download PDF
⟨ Previous Next ⟩

Abstract

Pseudo-parallel real hypersurfaces in complex space forms can be defined as an extrinsic analogues of pseudo-symmetric real hypersurfaces, that generalize the notion of semi-symmetric real hypersurface. In this paper a classification of the pseudo-parallel real hypersurfaces in a non-flat complex space forms is obtained.

Keywords

References

  1. A. C. Asperti, G. A. Lobos and F. Mercuri, Pseudo-parallel immersions in space forms, Mat. Contemp. 17 (1999), 59–70
  2. A. C. Asperti, G. A. Lobos and F. Mercuri, Pseudo-parallel submanifolds of a space form, Adv. Geom. 2 (2002), 57–71
  3. J. Berndt, Real hypersurfaces with constant principal curvatures in complex hyperbolic space, J. Reine Angew. Math. 395 (1989), 132–141
  4. M. do Carmo, M. Dacjzer and F. Mercuri, Compact conformally flat hypersurfaces, Trans. Amer. Math. Soc. 288 (1985), 189–205
  5. T. E. Cecil and P. J. Ryan, Tight and taut immersions of manifolds, Research Notes in Mathematics, vol. 107, Pitman, Boston, MA, 1985
  6. T. E. Cecil and P. J. Ryan, Focal sets and real hypersurfaces in complex projective space, Trans. Amer. Math. Soc. 269 (1982), 481–499
  7. J. Deprez, Semiparallel surfaces in Euclidean space, J. Geom. 25 (1985), 192–200
  8. J. Deprez, Semiparallel hypersurfaces, Rend. Sem. Mat. Univ. Politec. Torino, 44 (1986), 303–316
  9. J. Deprez, Semiparallel immersions. Geometry and topology of submanifolds (Marseille, 1987), 73–78, World Sci. Publishing, Teaneck, NJ, 1989
  10. R. Deszcz, On pseudosymmetric spaces, Bull. Soc. Math. Belg. Ser. A 44 (1992), 1–34
  11. F. Dillen, Semi-parallel hypersurfaces of a real space form, Israel J. Math. 75 (1991), 193–202
  12. D. Ferus, Symmetric submanifolds of Euclidean space, Math. Ann. 247 (1980), 81–93
  13. U. Lumiste, Semi-symmetric submanifold as the second order envelope of symmetric submanifolds, Proc. Estonian Acad. Sci., Phys. Math. 39 (1990), 1–8
  14. S. Maeda, Real hypersurfaces of complex projective spaces, Math. Ann. 263 (1983), 473–478
  15. S. Montiel, Real hypersurfaces of a complex hyperbolic space, J. Math. Soc. Japan 37 (1985), 515–535
  16. S. Montiel and A. Romero, On some real hypersurfaces of a complex hyperbolic space, Geom. Dedicata 20 (1986), 245–261
  17. H. Naitoh, Parallel submanifolds of complex space forms, I and II Nagoya Math. J. I 90, 85–117, II 91, (1983), 119–149
  18. R. Niebergall and P. J. Ryan, Semi-parallel and semi-symmetric real hypersurfaces in complex space forms, Kyungpook Math. J. 38 (1998), 227–234
  19. R. Niebergall and P. J. Ryan, Real hypersurfaces in complex space forms, Tight and taut submanifolds, 233–305, Math. Sci. Res. Inst. Publ. Vol. 32, Cambridge Univ. Press, Cambridge, 1997
  20. M. Ortega, Classifications of real hypersurfaces in complex space forms by means of curvature conditions, Bull. Belg. Math. Soc. Simon Stevin 3 (2002), 351–360
  21. R. Takagi, Real hypersurfaces in a complex projective space with constant principal curvature, J. Math. Soc. Japan 27 (1973), 43–53
  22. Y. Tashiro and S. Tachibana, On Fubinian and C-Fubinian manifolds, KodaiMath. Sem. Rep. 15 (1963), 176–183

Cited by

  1. The structure Jacobi operator and the shape operator of real hypersurfaces in $$\mathbb {C}P^{2}$$ C P 2 and $$\mathbb {C}H^{2}$$ C H 2 vol.55, pp.2, 2014, https://doi.org/10.1007/s13366-013-0174-2
  2. Pseudo-parallel Lagrangian submanifolds in complex space forms vol.27, pp.1, 2009, https://doi.org/10.1016/j.difgeo.2008.06.014