A characterization of complex hypersurfaces in $\textbf {C}^ m$
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- by Marcos Dajczer PDF
- Proc. Amer. Math. Soc. 105 (1989), 425-428 Request permission
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
- E. Artin, Geometric algebra, Interscience Publishers, Inc., New York-London, 1957. MR 0082463
- Marcos Dajczer and Detlef Gromoll, Gauss parametrizations and rigidity aspects of submanifolds, J. Differential Geom. 22 (1985), no. 1, 1–12. MR 826420 S. Kobayashi and K. Nomizu, Foundations of differential geometry, Interscience, New York, 1969.
- John Douglas Moore, Submanifolds of constant positive curvature. I, Duke Math. J. 44 (1977), no. 2, 449–484. MR 438256
Additional Information
- © Copyright 1989 American Mathematical Society
- 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