Nihonkai Mathematical Journal

Ricci pseudo $\eta$-parallel real hypersurfaces

Mayuko Kon

Full-text: Open access

Abstract

We prove that the Ricci tensor of a real hypersurface of a complex space form $M^n(c)$, $c\neq 0$, $n\geq 3$, satisfies Ricci pseudo $\eta$-parallel condition if and only if $M$ is pseudo-Einstein.

Article information

Source
Nihonkai Math. J., Volume 24, Number 1 (2013), 45-55.

Dates
First available in Project Euclid: 5 September 2013

Permanent link to this document
https://projecteuclid.org/euclid.nihmj/1378408116

Mathematical Reviews number (MathSciNet)
MR3114124

Zentralblatt MATH identifier
1285.53013

Subjects
Primary: 53B25: Local submanifolds [See also 53C40] 53C55: Hermitian and Kählerian manifolds [See also 32Cxx]
Secondary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)

Keywords
pseudo $\eta$-parallel Ricci tensor real hypersurface complex space form

Citation

Kon, Mayuko. Ricci pseudo $\eta$-parallel real hypersurfaces. Nihonkai Math. J. 24 (2013), no. 1, 45--55. https://projecteuclid.org/euclid.nihmj/1378408116


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References

  • T. E. Cecil and P. J. Ryan, Focal sets and real hypersurfaces in complex projective space, Trans. Amer. Math. Soc. 269 (1982), 481–499.
  • R. Deszcz and S. Yaprak, Curvature properties of Cartan hypersurfaces, Colloq. Math. 67 (1994), 91–97.
  • U.-H. Ki, Real hypersurfaces with parallel Ricci tensor of a complex space form, Tsukuba J. Math. 13 (1989), 73–81.
  • U.-H. Ki, H. Nakagawa and Y. J. Suh, Real hypersurfaces with harmonic Weyl tensor of a complex space form, Hiroshima Math. J. 20 (1990), 93–102.
  • I.-B. Ki, H. J. Park and H. Song, Ricci-pseudo-symmetric real hypersurfaces in complex space forms, Nihonkai Math. J. 18 (2007), 1–9.
  • M. Kimura and S. Maeda, On real hypersurfaces of a complex projective space, Math. Z., 202 (1989), 299–311.
  • Masahiro Kon, Pseudo-Einstein real hypersurfaces in complex space forms, J. Differential Geom. 14 (1979), 339–354.
  • Mayuko Kon, Ricci recurrent CR submanifolds of a comples space form, Tsukuba Journal of Mathematics 31 (2007), 233–252.
  • S. Montiel, Real hypersurfaces of a complex hyperbolic space, J. Math. Soc. Japan 37 (1985), 515–535.
  • R. Niebergall and P. J. Ryan, Real hypersurfaces in complex space forms. Tight and taut submanifolds, Tight and taut submanifolds 32 (1997), 233–305.
  • R. Takagi, Real hypersurfaces in a complex projective space with constant principal curvatures. J. Math. Soc. Japan 27 (1975), 43–53.
  • Y. Tashiro, S. Tachibana, On Fubinian and $C$-Fubinian manifolds, K$\rm{\bar{o}}$dai Math. Sem. Rep. 15 (1963), 176–183.