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Keywords:
real hypersurfaces; holomorphic and totally real sectional curvature
real hypersurfaces; holomorphic and totally real sectional curvature
Summary:
We characterize real hypersurfaces with constant holomorphic sectional curvature of a non flat complex space form as the ones which have constant totally real sectional curvature.
References:
[1] T. E. Cecil, P. J. Ryan: Focal sets and real hypersurfaces in complex projective space. Trans. Amer. Math. Soc. 269 (1982), 481–499. MR 0637703
[2] M. Kimura: Sectional curvatures of holomorphic planes on a real hypersurface in $P_nC$. Math. Ann. 276 (1987), 487–499. DOI 10.1007/BF01450843 | MR 0875342
[3] Y. Maeda: On real hypersurfaces of a complex projective space. J. Math. Soc. Japan 28 (1976), 529–540. DOI 10.2969/jmsj/02830529 | MR 0407772 | Zbl 0324.53039
[4] S. Montiel: Real hypersurfaces of complex hyperbolic space. J. Math. Soc. Japan 37 (1985), 515–535. DOI 10.2969/jmsj/03730515 | MR 0792990
[5] R. Niebergall, P. J. Ryan: Real hypersurfaces in complex space forms. Cambridge University Press. Math. Sci. Res. Inst. Publ. 32 (1997), 233–305. MR 1486875
[6] M. Ortega, J. D. Pérez: Constant holomorphic sectional curvature and type number of real hypersurfaces of complex hyperbolic space. Proc. 4th Internat. Congress of Geometry, Thessaloniki, 1996. MR 1470995
[7] D. J. Sohn, Y. J. Suh: Classification of real hypersurfaces in complex hyperbolic space in terms of constant $\phi $-holomorphic sectional curvature. Kyungpook Math. J. 35 (1996), 801–819. MR 1678228
[8] Y. J.Suh: A characterization of ruled real hypersurfaces in $P_nC$. J. Korean Math. Soc. 29 (1992), 351–359. MR 1180662
[9] M. H. Vernon: Contact hypersurfaces of complex hyperbolic space. Tôhoku Math. J. 39 (1987), . DOI 10.2748/tmj/1178228324 | MR 0887937
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