Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

ON CHARACTERIZATIONS OF REAL HYPERSURFACES WITH ${\eta}-PARALLEL$ RICCI OPERATORS IN A COMPLEX SPACE FORM

  • Kim, In-Bae (DEPARTMENT OF MATHEMATICS, HANKUK NUINERSITY OF FOREIGN STUDIES) ;
  • Park, Hye-Jeong (DEPARTMENT OF MATHEMATICS, HANKUK NUINERSITY OF FOREIGN STUDIES) ;
  • Sohn, Woon-Ha (DEPARTMENT OF MATHEMATICS, HANKUK NUINERSITY OF FOREIGN STUDIES)
  • Published : 2006.05.01
Download PDF
⟨ Previous Next ⟩

Abstract

We shall give a characterization of a real hypersurface M in a complex space form Mn(c), $c\;{\neq}\;0$, whose Ricci operator and structure tensor commute each other on the holomorphic distribution of M, and the Ricci operator is ${\eta}-parallel$.

Keywords

References

  1. C. Baikoussis, A characterization of real hypersurfaces in complex space forms in terms of the Ricci tensor, Canad. Math. Bull. 40 (1997), no. 3, 257-265 https://doi.org/10.4153/CMB-1997-031-5
  2. J. Berndt, Real hypersurfaces with constant principal curvatures in complex hy- perbolic space, J. Reine Angew Math. 395 (1989), 132-141
  3. M. Kimura and S. Maeda, On real hypersurfaces of a complex projective space, Math. Z. 202 (1989), no. 3, 299-311 https://doi.org/10.1007/BF01159962
  4. M. Kimura and S. Maeda, Characterizations of geodesic hyperspheres in a complex projective space in terms of Ricci tensors, Yokohama Math. J. 40 (1992), no. 1, 35-43
  5. R. Niebergall and P. J. Ryan, Real hypersurfaces in complex space forms: in Tight and taut submanifolds,, Math. Sci. Res. Inst. Publ., 32., 233-305 Publications, Cambridge, 1997
  6. Y. J. Suh, On real hypersurfaces of a complex space form with $\eta$-parallel Ricci tensor, Tsukuba J. Math. 14 (1990), no. 1, 27-37 https://doi.org/10.21099/tkbjm/1496161316
  7. R. Takagi, On homogeneous real hypersurfaces in a complex projective space, Osaka J. Math. 10 (1973), 495-506
  8. R. Takagi, I. -B. Kim and B. H. Kim, The rigidity for real hypersurfaces in a complex projective space, Tohoku Math. J. (2) 50 (1998), no. 4, 531-536 https://doi.org/10.2748/tmj/1178224896
  9. T. Taniguchi, Characterizations of real hypersurfaces of a complex hyperbolic space in terms of Ricci tensor and holomorphic distribution, Tsukuba J. Math. 18 (1994), no. 2, 469-482 https://doi.org/10.21099/tkbjm/1496162613

Cited by

  1. A study of real hypersurfaces with Ricci operators in 2-dimensional complex space forms vol.266, pp.2, 2013, https://doi.org/10.2140/pjm.2013.266.305