ON NON-PROPER PSEUDO-EINSTEIN RULED REAL HYPERSURFACES IN COMPLEX SPACE FORMS

Abstract

In the paper [12] we have introduced the new kind of pseudo-einstein ruled real hypersurfaces in complex space forms $M_n(c), c\neq0$, which are foliated by pseudo-Einstein leaves. The purpose of this paper is to give a geometric condition for non-proper pseudo-Einstein ruled real hypersurfaces to be totally geodesic in the sense of Kimura [8] for c> and Ahn, Lee and the present author [1] for c<0.

Keywords

• Einstein;
• pseudo-Einstein ruled real hypersurface;
• complex space form;
• Ricci tensor;
• totally geodesic

File

Download PDF

References

1. J. Math. v.17 On ruled real hypersurfaces in a complex space form S. S. Ahn;S. B. Lee;Y. J. Suh
2. J. Reine Angew. Math. v.395 Real hypersurfaces with constant principal curvatures in a complex hyperbolic space J. Berndt
3. Geometry and Topology of submanifolds II J. Berndt
4. Trans. Amer. Math. Soc. v.269 Focal sets and real hypersurfaces in complex projective space T. E. Cecil;P. J. Ryan
5. Math. J. Okayama v.32 On real hypersurfaces of a complex space form U-H. Ki;Y. J. Suh
6. Canadian Math. Bull. v.37 On a characterization of real hypersurfaces of type A in a complex space form U-H. Ki;Y. J. Suh
7. Trans Amer. Math. Soc. v.296 Real hypersurfaces and complex submanifolds in complex projective space M. Kimura
8. Math. Ann. v.276 sectional curvatures of a holomorphic plane in Pn(C) M. Kimura
9. Math. Z. v.202 On real hypersurfaces of a complex projective space M. Kimura;S. Maeda
10. J. Math. Soc. Japan. v.28 On real hypersurfaces of a complex projective space Y. Maeda
11. J. Math. Soc. Japan v.37 Real hypersurfaces of a complex hyperbolic space S. Montiel
12. to appear in Note di Matematica v.19 On pseudo Einstein ruled real hypersurfaces in complex space forms Y. J. Suh
13. Nihonkai Math. J. v.6 Characterizations of real hypersurfaces in complex space forms in terms of Weingarten map Y. J. Suh
14. Osaka J. Math. v.10 On homogeneous real hypersurfaces of a complex projective space R. Takagi