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Proceedings of the American Mathematical Society

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

 

 

$ {\rm O}(2)\times{\rm O}(2)$-invariant hypersurfaces with constant negative scalar curvature in $ E\sp 4$


Author: Takashi Okayasu
Journal: Proc. Amer. Math. Soc. 107 (1989), 1045-1050
MSC: Primary 53C40
MathSciNet review: 990430
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Abstract: We use the method of equivariant differential geometry to prove the existence of a complete hypersurface with constant negative scalar curvature in $ {E^n}(n \geq 4)$. This is the first example of a complete hypersurface with constant negative scalar curvature in $ {E^n}(n \geq 4)$.


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DOI: https://doi.org/10.1090/S0002-9939-1989-0990430-7
Keywords: Hypersurface, scalar curvature, Euclidean space, equivariant differential geometry
Article copyright: © Copyright 1989 American Mathematical Society