Hostname: page-component-7c8c6479df-p566r Total loading time: 0 Render date: 2024-03-18T09:26:23.036Z Has data issue: false hasContentIssue false

On Characterizations of Real Hypersurfaces in a Complex Space Form with η-Parallel Shape Operator

Published online by Cambridge University Press:  20 November 2018

S. H. Kon
Affiliation:
Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Malaysia e-mail: shkon@um.edu.mylooth@um.edu.my
Tee-How Loo
Affiliation:
Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Malaysia e-mail: shkon@um.edu.mylooth@um.edu.my
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.

In this paper we study real hypersurfaces in a non-flat complex space form with $\eta $-parallel shape operator. Several partial characterizations of these real hypersurfaces are obtained.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2012

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] Berndt, J., Real hypersurfaces with constant principal curvatures in complex hyperbolic space. J. Reine Angew Math. 395(1989), 132141.Google Scholar
[3] Choe, Y.-W., Characterization of certain real hypersurfaces of a complex space form. Nihonkai Math. J. 6(1995), no. 1, 97114.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. doi:10.4153/CMB-1994-035-8Google Scholar
[5] Kim, I.-B., Kim, K. H. and Sohn, W. H., Characterizations of real hypersurfaces in a complex space form. Canad. Math. Bull. 50(2007), no. 1, 97104. doi:10.4153/CMB-2007-009-5Google Scholar
[6] Kim, H. S. and Pyo, Y.-S., On real hypersurfaces of type A in a complex space form. III. Balkan J. Geom. Appl. 3(1998), no. 2, 101110.Google Scholar
[7] Kimura, M., Real hypersurfaces and complex submanifolds in complex projective space. Trans. Amer. Math. Soc. 296(1986), no. 1, 137149. doi:10.1090/S0002-9947-1986-0837803-2Google Scholar
[8] Kimura, M. and Maeda, S., On real hypersurfaces of a complex projective space. Math. Z. 202(1989), no. 3, 299311. doi:10.1007/BF01159962Google Scholar
[9] Kon, M., Pseudo-Einstein real hypersurfaces in complex space forms. J. Diff. Geom. 14(1979), no. 3, 339354.Google Scholar
[10] Lohnherr, M. and Reckziegel, H., On ruled real hypersurfaces in complex space forms. Geom. Dedicata. 74(1999), no. 3, 267286. doi:10.1023/A:1005000122427Google Scholar
[11] Maeda, Y., On real hypersurfaces of a complex projective space. J. Math. Soc. Japan 28(1976), no. 3, 529540. doi:10.2969/jmsj/02830529Google Scholar
[12] Montiel, S. and Romero, A., On some real hypersurfaces of a complex hyperbolic space. Geom. Dedicata. 20(1986), no. 2, 245261.Google Scholar
[13] Niebergall, R. and Ryan, P. J., Real hypersurfaces in complex space forms. In : Tight and Taut Submanifolds, Math. Sci., Res. Inst. Publ. 32, Cambrigde University Press, Cambridge, 1997, pp. 233305.Google Scholar
[14] Okumura, M., Contact hypersurfaces in certain Kaehlerian manifolds. Tohoku Math. J. 18(1966), 74102. doi:10.2748/tmj/1178243483Google Scholar
[15] Okumura, M., On some real hypersurfaces of a complex projective space. Trans. Amer. Math. Soc. 212(1975), 355364. doi:10.1090/S0002-9947-1975-0377787-XGoogle Scholar
[16] Suh, Y. J., Characterizations of real hypersurfaces in complex space forms in terms of Weingarten map. Nihonkai Math. J. 6(1995), no. 1, 6379.Google Scholar
[17] Suh, Y. J., On real hypersurfaces of a complex space form with η-parallel Ricci tensor. Tsukuba J. Math. 14(1990), no. 1, 2737.Google Scholar
[18] Takagi, R., On homogeneous real hypersurfaces in a complex projective space. Osaka J. Math. 10(1973), 495506.Google Scholar
[19] Vernon, M. H., Contact hypersurfaces of a complex hyperbolic space. Tohoku Math. J. 39(1987), no. 2, 215222. doi:10.2748/tmj/1178228324Google Scholar