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Remarks on the curvature of hypersurfaces in Cn

Published online by Cambridge University Press:  22 January 2016

Takeshi Sasaki  and
Kiyoshi Shiga
Takeshi Sasaki
Affiliation:
Nagoya University
Kiyoshi Shiga
Affiliation:
Gifu University
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In this paper we shall study the global condition of curvatures of hypersurfaces in the complex Euclidean space. S. Bochner ([1]) and E. Calabi ([2]) have already investigated kähler embeddings (i.e. holomorphic and isometric embeddings) of a kähler manifold into the complex Euclidean space. However, it seems that they did not discuss the relation between the embeddability and the curvature.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 71 , November 1978 , pp. 91 - 95
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1978

References

[1] Bochner, S., Curvature in hermitian metric, Bull. Amer. Math. Soc, 53 (1947), 179–195.CrossRefGoogle Scholar
[2] Galabi, E., Isometric imbedding of complex manifolds, Ann. of Math., 58 (1953), 1–23.Google Scholar
[3] Kobayashi, S. and Nomizu, K., Foundations of differential geometry, vol. II (1969), Interscience publishers.Google Scholar
[4] Vitter, A., On the curvature of complex hypersurfaces, Indiana Univ. Math. J., 23 (1974), 813–826.CrossRefGoogle Scholar