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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A characterization of complex hypersurfaces in $ {\bf C}\sp m$


Author: Marcos Dajczer
Journal: Proc. Amer. Math. Soc. 105 (1989), 425-428
MSC: Primary 53C42
DOI: https://doi.org/10.1090/S0002-9939-1989-0946632-9
MathSciNet review: 946632
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Abstract: We show that an isometric immersion of a connected Kaehler manifold $ {M^{2n}}$ into the euclidean space with (real) codimension two is holomorphic with respect to some complex structure of $ {{\mathbf{R}}^{2n + 2}}$ provided that the index of nullity $ \mu $ of the curvature tensor satisfies $ \mu < 2n - 4$ everywhere.


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DOI: https://doi.org/10.1090/S0002-9939-1989-0946632-9
Article copyright: © Copyright 1989 American Mathematical Society