Hostname: page-component-7c8c6479df-fqc5m Total loading time: 0 Render date: 2024-03-19T06:05:55.974Z Has data issue: false hasContentIssue false

Two Conditions on the Structure Jacobi Operator for Real Hypersurfaces in Complex Projective Space

Published online by Cambridge University Press:  20 November 2018

Juan de Dios Pérez
Affiliation:
Departamento de Geometría y Topología, Universidad de Granada, 18071 Granada, Spain e-mail: jdperez@ugr.es
Young Jin Suh
Affiliation:
Department of Mathematics, Kyungpook National University, Taegu 702-701, Republic of Korea e-mail: yjsuh@knu.ac.kr
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 classify real hypersurfaces in complex projective space whose structure Jacobi operator satisfies two conditions at the same time.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2011

References

[1] Baikoussis, C., A characterization of real hypersurfaces in complex space forms in terms of the Ricci tensor. Canad. Math. Bull. 40(1997), 257265. doi:10.4153/CMB-1997-031-5Google Scholar
[2] Cecil, T. E. and Ryan, P. J., Focal sets and real hypersurfaces in complex projective space. Trans. Amer. Math. Soc. 269(1982), 481499.Google Scholar
[3] 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), 238244. doi:10.4153/CMB-1994-035-8Google Scholar
[4] Kimura, M., Sectional curvatures of holomorphic planes on a real hypersurface in Pn (ℂ) . Math. Ann. 276(1987), 487497. doi:10.1007/BF01450843Google Scholar
[5] Lee, H. J., de Dios Pérez, J., Santos, F. G., and Suh, Y. J., On the structure Jacobi operator of a real hypersurface in complex projective space. Monatsh. Math. 158(2009), no. 2, 187194. doi:10.1007/s00605-008-0025-7Google Scholar
[6] 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
[7] Suh, Y. J., A characterization of ruled real hypersurfaces in Pn(C) . J. Korean Math. Soc. 29(1992), 351359.Google Scholar
[8] Takagi, R., Real hypersurfaces in a complex projective space with constant principal curvatures. J. Math. Soc. Japan 27(1975), 4353. doi:10.2969/jmsj/02710043Google Scholar
[9] Takagi, R., Real hypersurfaces in a complex projective space with constant principal curvatures II. J. Math. Soc. Japan 27(1975), 507516. doi:10.2969/jmsj/02740507Google Scholar