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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.


References [Enhancements On Off] (What's this?)

  • [A] M. Artin, Geometric algebra, Interscience, New York, 1957. MR 0082463 (18:553e)
  • [D-G] M. Dajczer and D. Gromoll, Real Kaehler submanifolds and uniqueness of the Gauss map, J. Differential Geom. 22 (1985), 13-28. MR 826421 (87g:53088b)
  • [K-N] S. Kobayashi and K. Nomizu, Foundations of differential geometry, Interscience, New York, 1969.
  • [M] J. D. Moore, Submanifolds of constant positive curvature. I, Duke Math. J. 44 (1977), 449-484. MR 0438256 (55:11174)

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

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