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Proceedings of the American Mathematical Society

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Shape operators of Einstein hypersurfaces in indefinite space forms


Author: Martin A. Magid
Journal: Proc. Amer. Math. Soc. 84 (1982), 237-242
MSC: Primary 53C25; Secondary 53B30, 53C42
DOI: https://doi.org/10.1090/S0002-9939-1982-0637176-6
MathSciNet review: 637176
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Abstract: The possible shape operators for an Einstein hypersurface in an indefinite space form are classified algebraically. If the shape operator $ A$ is not diagonalizable then either $ {A^2} = 0$ or $ {A^2} = - {b^2}{\text{Id}}$.


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

  • [F] Aaron Fialkow, Hypersurfaces of a space of constant curvature, Ann. of Math. (2) 39 (1938), no. 4, 762–785. MR 1503435, https://doi.org/10.2307/1968462
  • [G] L. Graves, Codimension-one isometric immersions between Lorentz spaces, Thesis, Brown University, 1977.
  • [M] M. Magid, Indefinite Einstein hypersurfaces (preprint).
  • [P] A. Z. Petrov, Einstein spaces, Translated from the Russian by R. F. Kelleher. Translation edited by J. Woodrow, Pergamon Press, Oxford-Edinburgh-New York, 1969. MR 0244912

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0637176-6
Article copyright: © Copyright 1982 American Mathematical Society