# NONEXISTENCE OF RICCI-PARALLEL REAL HYPERSURFACES IN P2C OR H2C

• Kim, Un-Kyu (Department of Mathematics Education, College of Education, Sungkyunkwan University)
• Published : 2004.11.01

#### Abstract

Niebergall and Ryan posed many open problems on real hypersurfaces in complex space forms. One of them is "Are there any Ricci-parallel real hypersurfaces in complex projective space $P_2C$ or complex hyperbolic space $H_2C$\ulcorner" The purpose of present paper is to prove the nonexistence of such hypersurfaces.

#### References

1. D. E. Blair, Contact manifolds in Riemannian Geometry, Lecture Notes in Math. 509, Springer-Verlag, Berlin. Heidelberg.New York, 1976
2. R. Niebergall and P. J. Ryan, Real hypersurfaces in complex space forms, 233–305 in Tight and Taut Submanifolds, edited by T. E. Cecil et al., MSRI Publications, Cambridge., 1997
3. Un Kyu Kim, Some problems on 3-dimensional real hypersurfaces in complex space forms, Commun. Korean Math. Soc. 16 (2001), no. 2, 253–263

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