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CERTAIN RESULTS OF REAL HYPERSURFACES IN A COMPLEX SPACE FORM

Published online by Cambridge University Press:  02 August 2011

AMALENDU GHOSH*
Affiliation:
Department of Mathematics, Krishnagar Government College, Krishnagar: 741101, W.B., India e-mail: aghosh_70@yahoo.com
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Abstract

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First, we classify a real hypersurface of a non-flat complex space form with (i) semi-parallel T(=£ξg), and (ii) recurrent T. Next, we characterise a real hypersurface admitting the generalised η-Ricci soliton in a non-flat complex space form.

Keywords

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2011

References

REFERENCES

1.Berndt, J., Real hypersurfaces with constant principal curvatures in complex hyperbolic space, J. Reine Angew. Math. 395 (1989), 132141.Google 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.Cho, J. T. and Kimura, M., Ricci solitons and real hypersurfaces in a complex space form, Tohoku Math. J. 61 (2) (2009), 205212.CrossRefGoogle Scholar
4.Chow, B. and Knopf, D., The Ricci flow: An introduction, Mathematical Surveys and Monographs, Vol. 110 (American Mathematical Society, Providence, RI, 2004).CrossRefGoogle Scholar
5.Ki, U-H., On real hypersurfaces with parallel Ricci tensor of a complex space form, Tsukuba J. Math. 13 (1989), 7381.CrossRefGoogle Scholar
6.Ki, U-H. and Suh, Y. J., On real hypersurfaces of a complex space form, Math. J. Okayama Univ. 32 (1990), 207221.Google Scholar
7.Kim, U. K., Nonexistence of Ricci-parallel real hypersurfaces in P 2C or H 2C, Bull. Korean Math. Soc. 41 (2004), 699708.CrossRefGoogle Scholar
8.Kim, H. S. and Ryan, P. J., A classification of pseudo-Einstein hypersurfaces in CP 2, Diff. Geom. Appl. 26 (2008), 106112.CrossRefGoogle Scholar
9.Kimura, M., Real hypersurfaces and complex submanifolds in complex projective space, Trans. Amer. Math. Soc. 296 (1986), 137149.CrossRefGoogle Scholar
10.Kon, M., Pseudo-Einstein real hypersurfaces in complex space forms, J. Diff. Geom. 14 (1979), 339354.Google Scholar
11.Maeda, Y., On real hypersurfaces of a complex projective space, J. Math. Soc. Japan 28 (1976), 529540.CrossRefGoogle Scholar
12.Montiel, S., Real hypersurfaces of a complex hyperbolic space, J. Math. Soc. Japan 37 (1985), 515535.CrossRefGoogle Scholar
13.Montiel, S. and Romero, A., On some real hypersurfaces of a complex hyperbolic space, Geom. Dedicata 20 (1986), 245261.CrossRefGoogle Scholar
14.Niebergall, R. and Ryan, P. J., Real hypersurfaces in complex space forms, in Tight and taut submanifolds (Cecil, T. E. et al. , Editors) (MSRI, Cambridge, UK, 1994), 233305.Google Scholar
15.Okumura, M., On some real hyersurfaces of a complex projective space, Trans. Amer. Math. Soc. 212 (1975), 355364.CrossRefGoogle Scholar
16.Pyo, Y.-S. and Suh, Y. J., Characterizations of real hypersurfaces in complex space forms in terms of curvature tensors, Tsukuba J. Math. 19 (1995), 163172.CrossRefGoogle Scholar
17.Takagi, R., On homogeneous real hypersurfaces of a complex projective space, Osaka J. Math. 10 (1973), 495506.Google Scholar
18.Takagi, R., Real hypersurfaces in a complex projective space with constant principal curvatures I, II, J. Math. Soc. Japan, 27 (1975), 4353, 507–516.Google Scholar