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Einstein-Kaehler Manifolds Immersed in a Complex Projective Space

Published online by Cambridge University Press:  20 November 2018

Hisao Nakaga
Hisao Nakaga*
Affiliation:
Tokyo University of Agriculture and Technology, Tokyo, Japan
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A Kaehler manifold of constant holomorphic curvature is called a complex space form. By a Kaehler submanifold we mean a complex submanifold with the induced Kaehler metric. B. Smyth [5] has studied a complete Einstein- Kaehler hypersurface in a complete and simply connected complex space form and classified completely the hypersurface. The local version of this result has been shown to be true by S. S. Chern [1], and partially by T. Takahashi [6] independently.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 1 , 01 February 1976 , pp. 1 - 8
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Chern, S. S., Einstein hyper surfaces in a Kaehlerian manifold of constant holomorphic curvature, J. Differential Geometry 1 (1967), 21–31.Google Scholar
2. Nakagawa, H. and Takagi, R., On symmetric Kaehler submanifolds in a complex projective space (to appear).Google Scholar
3. Nomizu, K. and Smyth, B., Differential geometry of complex hyper surf aces II, J. Math. Soc. Japan 20 (1968), 498–527.Google Scholar
4. Ogiue, K., Differential geometry of Kaehler submanifolds, Advances in Math. 13 (1974), 73–114.Google Scholar
5. Smyth, B., Differential geometry of complex hyper surf aces, Ann. of Math. 85 (1967), 246–266.Google Scholar
6. Takahashi, T., Hyper surfaces with parallel Ricci tensor in a space of constant holomorphic sectional curvature, J. Math. Soc. Japan 19 (1967), 199–204.Google Scholar