Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-24T02:10:50.334Z Has data issue: false hasContentIssue false

Characterizations of Real Hypersurfaces in a Complex Space Form

Published online by Cambridge University Press:  20 November 2018

In-Bae Kim
Affiliation:
Department of Mathematics, Hankuk University of Foreign Studies, Seoul 130-791, Korea e-mail: [email protected]@[email protected]
Ki Hyun Kim
Affiliation:
Department of Mathematics, Hankuk University of Foreign Studies, Seoul 130-791, Korea e-mail: [email protected]@[email protected]
Woon Ha Sohn
Affiliation:
Department of Mathematics, Hankuk University of Foreign Studies, Seoul 130-791, Korea e-mail: [email protected]@[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 a real hypersurface $M$ in a complex space form ${{M}_{n}}\left( c \right),c\ne 0$, whose shape operator and structure tensor commute each other on the holomorphic distribution of M.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2007

References

[1] Ahn, S. S., Lee, S. B., and Suh, Y. J., On ruled real hypersurfaces in a complex space form. Tsukuba J. Math. 17(1993), no. 2, 311322.Google Scholar
[2] Baikoussis, C., A characterization of real hypersurfaces in complex space form in terms of the Ricci tensor. Canad. Math. Bull. 40(1997), no. 3, 257265.Google Scholar
[3] Berndt, J., Real hypersurfaces with constant principal curvatures in a complex hyperbolic space. J. Reine AngewMath. 359(1989), 132141.Google Scholar
[4] 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), no. 2, 238244.Google Scholar
[5] Kimura, M. and Maeda, S., On real hypersurfaces of a complex projective space. Math. Z. 202(1989), no. 3, 299311.Google Scholar
[6] Montiel, S. and Romero, A., On some real hypersurfaces of a complex hyperbolic space. Geom. Dedicata 20(1986), no. 2, 245261.Google Scholar
[7] Niebergall, R. and Ryan, P. J., Real hypersurfaces in complex space forms. In: Tight and Taut Submanifolds, Math. Sci. Res. Inst. Publ. 32, Cambridge Univiversity Press, Cambridge, 1997, pp. 233305.Google Scholar
[8] Okumura, M., On some real hypersurfaces of a complex projective space. Trans. Amer. Math. Soc. 212(1975), 355364.Google Scholar
[9] Takagi, R., On homogeneous real hypersurfaces of a complex projective space. Osaka J. Math. 10(1973), 495506.Google Scholar
[10] Takagi, R., Kim, I.-B. and Kim, B. H., The rigidity for real hypersurfaces in a complex projective space. Tohoku Math. J. 50(1998), no. 4, 531536.Google Scholar