Shape operators of Einstein hypersurfaces in indefinite space forms
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- by Martin A. Magid PDF
- Proc. Amer. Math. Soc. 84 (1982), 237-242 Request permission
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
- Aaron Fialkow, Hypersurfaces of a space of constant curvature, Ann. of Math. (2) 39 (1938), no. 4, 762–785. MR 1503435, DOI 10.2307/1968462 L. Graves, Codimension-one isometric immersions between Lorentz spaces, Thesis, Brown University, 1977. M. Magid, Indefinite Einstein hypersurfaces (preprint).
- A. Z. Petrov, Einstein spaces, Pergamon Press, Oxford-Edinburgh-New York, 1969. Translated from the Russian by R. F. Kelleher; Translation edited by J. Woodrow. MR 0244912
Additional Information
- © Copyright 1982 American Mathematical Society
- 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