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http://dx.doi.org/10.4134/BKMS.2015.52.1.335

NOTES ON REAL HYPERSURFACES IN A COMPLEX SPACE FORM  

Cho, Jong Taek (Department of Mathematics Chonnam National University)
Publication Information
Bulletin of the Korean Mathematical Society / v.52, no.1, 2015 , pp. 335-344 More about this Journal
Abstract
We characterize a homogeneous real hypersurface of type (A) or a ruled real hypersurface in a non-flat complex space form, respectively.
Keywords
real hypersurface; complex space form; almost contact structure;
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1 T. Adachi, M. Kameda, and S. Maeda, Real hypersurfaces which are contact in a nonflat complex space form, Hokkaido Math. J. 40 (2011), no. 2, 205-217.   DOI
2 S.-S. Ahn, S.-B. Lee, and Y. J. Suh, On ruled real hypersurfaces in a complex space form, Tsukuba J. Math. 17 (1993), no. 2, 311-322.   DOI
3 J. Berndt, Real hypersurfaces with constant principal curvatures in complex hyperbolic space, J. Reine Angew. Math. 395 (1989), 132-141.
4 D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Progress in Math. 203, Birkhauser Boston, Inc., Boston, second edition, 2010.
5 D. E. Blair, Almost contact manifolds with Killing structure tensors, Pacific J. Math. 39 (1971), no. 2, 285-292.   DOI
6 T. E. Cecil and P. J. Ryan, Focal sets and real hypersurfaces in complex projective space, Trans. Amer. Math. Soc. 269 (1982), no. 2, 481-499.   DOI
7 J. T. Cho and J. Inoguchi, Contact metric hypersurfaces in complex space forms, Proceedings of the workshop on Differential Geometry of Submanifolds and Related Topics, Saga, August 4-6, 2012.
8 J. T. Cho and M. Kimura, Transversal symmetries on real hypersurfaces in a complex space form, Hiroshima Math. J. 43 (2013), no. 2, 223-238.
9 G. Dileo and A. M. Pastore, Almost Kenmotsu manifolds and local symmetry, Bull. Belg. Math. Soc. Simon Stevin 14 (2007), no. 2, 343-354.
10 S. I. Goldberg and K. Yano, Integrability of almost cosymplectic structures, Pacific J. Math. 31 (1969), 373-381.   DOI
11 S. Kanemaki, Quasi-Sasakian manifolds, Tohoku Math. J. 29 (1977), no. 2, 227-233.   DOI
12 K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J. 24 (1972), 93-103.   DOI
13 U.-H. Ki and Y. J. Suh, On real hypersurfaces of a complex space form, Math. J. Okayama Univ. 32 (1990), 207-221.
14 U.-H. Ki and Y. J. Suh, On a characterization of real hypersurfaces of type A in a complex space form, Canad. Math. Bull. 37 (1994), no. 2, 238-244.   DOI
15 M. Kimura, Real hypersurfaces and complex submanifolds in complex projective space, Trans. Amer. Math. Soc. 296 (1986), no. 1, 137-149.   DOI   ScienceOn
16 M. Kimura, Sectional curvatures of holomorphic planes on a real hypersurfaces in $P^n({\mathbb{C}})$, Math. Ann. 276 (1987), no. 3, 487-497.   DOI
17 M. Kon, Pseudo-Einstein real hypersurfaces in complex space forms, J. Diffential Geometry 14 (1979), no. 3, 339-354.   DOI
18 S. H. Kon and T. H. Loo, Real hypersurfaces in a complex space form with ${\eta}$-parallel shape operator, Math. Z. 269 (2011), no. 1-2, 47-58.   DOI
19 Y. Maeda, On real hypersurfaces of a complex projective space, J. Math. Soc. Japan 28 (1976), no. 3, 529-540.   DOI
20 S. Maeda and S. Udagawa, Real hypersurfaces of a complex projective space in terms of holomorphic distribution, Tsukuba J. Math. 14 (1990), no. 1, 39-52.   DOI
21 S. Montiel and A. Romero, On some real hypersurfaces of a complex hyperbolic space, Geom. Dedicata 20 (1986), no. 2, 245-261.   DOI
22 R. Niebergall and P. J. Ryan, Real hypersurfaces in complex space forms, Tight and taut submanifolds (Berkeley, CA, 1994), 233-305, Math. Sci. Res. Inst. Publ., 32, Cambridge Univ. Press, Cambridge, 1997.
23 M. Okumura, Certain almost contact hypersurfaces in Kaehlerian manifolds of constant holomorphic sectional curvature, Tohoku Math. J. (2) 16 (1964), 270-284.   DOI
24 Y. J. Suh, On real hypersurfaces of a complex space form with ${\eta}$-parallel Ricci tensor, Tsukuba J. Math. 14 (1990), no. 1, 27-37.   DOI
25 M. Okumura, On some real hypersurfaces of a complex projective space, Trans. Amer. Math. Soc. 212 (1975), 355-364.   DOI
26 M. Okumura, Compact real hypersurfaces of a complex projective space, J. Differential Geom. 12 (1977), no. 4, 595-598.   DOI
27 Z. Olszak, Curvature properties of quasi-Sasakian manifolds, Tensor (N.S.) 38 (1982), 19-28.
28 R. Takagi, On homogeneous real hypersurfaces in a complex projective space, Osaka J. Math. 19 (1973), 495-506.
29 R. Takagi, Real hypersurfaces in a complex projective space with constant principal curvatures I, II, J. Math. Soc. Japan 15 (1975), 43-53, 507-516.