Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-09T07:54:15.127Z Has data issue: false hasContentIssue false
  • English
  • Français

A Characterization of Real Hypersurfaces in Complex Space Forms in Terms of the Ricci Tensor

Published online by Cambridge University Press:  20 November 2018

Christos Baikoussis
Christos Baikoussis*
Affiliation:
Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece, e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We study real hypersurfaces of a complex space form Mn(c), c ≠ 0 under certain conditions of the Ricci tensor on the orthogonal distribution T0.

Keywords

Primary: 53C40secondary: 53C15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 40 , Issue 3 , 01 September 1997 , pp. 257 - 265
Copyright
Copyright © Canadian Mathematical Society 1997

References

1. Berndt, J., Real hypersurfaces with constant principal curvatures in complex hyperbolic space, J. Reine Angew. Math. 395 (1989), 132–141.Google Scholar
2. Berndt, J., Real hypersurfaces with constant principal curvatures in complex space forms, Geometry and Topology of Submanifolds II, Avignon 1988, 10–19, World Scientific, 1990.Google Scholar
3. Cecil, T. E. and Ryan, P. J., Focal sets and real hypersurfaces in complex projective space, Trans. Amer. Math. Soc. 269 (1982), 481–499.Google Scholar
4. Chen, B. Y., Differential geometry of real submanifolds in a Kaehlerian manifold, Mh. Math. 91 (1981), 257–274.Google Scholar
5. Chen, B. Y., Ludden, G. D. and S. Montiel, Real submanifolds in a Kaehlerian manifold, Algebras Groups Geom. 1 (1984), 174–216.Google Scholar
6. Ki, U.-H. and Suh, Y. J., On real hypersurfaces of a complex projective space, Math. J. Okayama Univ. 32 (1990), 207–221.Google Scholar
7. Ki, U.-H. and Suh, Y. J., On a characterization of real hypersurfaces of type A in a complex space form, Canad.Math. Bull. 37 (1994), 238–244.Google Scholar
8. Kimura, M., Real hypersurfaces in complex projective space, Trans. Amer.Math. Soc. 296 (1986), 137–149.Google Scholar
9. Kimura, M., Some real hypersurfaces in a complex projective space, Saitama Math. J. 5 (1987), 1–5.Google Scholar
10. Kimura, M., Correction to “Some real hypersurfaces in a complex projective space”, Saitama Math. J. 10 (1992), 33–34.Google Scholar
11. Kimura, M. and Maeda, S., Characterizations of geodesic hyperpheres in a complex projective space in terms of Ricci tensors, Yokohama Math. J. 40 (1992), 35–43.Google Scholar
12. Kimura, M. and Maeda, S., On real hypersurfaces of a complex projective space III, Hokkaido Math. J. 22 (1993), 63–78.Google Scholar
13. Kon, M., Pseudo-Einstein real hypersurfaces in complex space form, J. Differential Geom. 14 (1979), 339–354.Google Scholar
14. Maeda, S., Geometry of submanifolds which are neither Kaehler nor totally real in complex projective space, Bull. Nagoya Inst. Tech. 45 (1993), 1–50.Google Scholar
15. Maeda, S., Ricci tensors of real hypersurfaces in a complex projective space, Proc. Amer. Math. Soc. 122 (1994), 1229–1235.Google Scholar
16. Montiel, S., Real hypersurfaces of a complex hyperbolic space, J. Math. Soc. Japan 37 (1985), 515–535.Google Scholar
17. Montiel, S. and Romero, A., On some real hypersurfaces of a complex hyperbolic space, Geom. Dedicata 20 (1986), 245–261.Google Scholar
18. Okumura, M., On some real hypersurfaces of a complex projective space, Trans. Amer. Math. Soc. 212 (1975), 355–364.Google Scholar
19. Takagi, R., On homogeneous real hypersurfaces in a complex projective space, Osaka J. Math. 10 (1973), 495–506.Google Scholar
20. Taniguchi, T., Characterizations of real hypersurfaces of a complex hyperbolic space in terms of Ricci tensor and holomorphic distribution, Tsukuba J. Math. 18 (1994), 469–482 Google Scholar