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On Some Complex Submanifolds in Kaehler Manifolds

Published online by Cambridge University Press:  20 November 2018

Masahiro Kon
Masahiro Kon*
Affiliation:
Science University of Tokyo, Tokyo, Japan
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The purpose of this paper is to give some conditions for complex submanifolds in a Kaehler manifold of constant holomorphic sectional curvature to be Einstein.

For a complex hypersurface which is Einstein, Smyth [8] has obtained its classification and Chern [2] has proved the corresponding local result. Moreover, Takahashi [9] and Nomizu-Smyth [3] generalized this to a complex hypersurface with parallel Ricci tensor. We shall consider a condition weaker than the requirement that the Ricci tensor be parallel, that is we shall consider a complex submanifold with commuting curvature and Ricci operator, which condition was treated by Bishop-Goldberg [1].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 6 , December 1974 , pp. 1442 - 1449
Copyright
Copyright © Canadian Mathematical Society 1974

References

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