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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Rigidity for complete Weingarten hypersurfaces


Authors: M. Dajczer and K. Tenenblat
Journal: Trans. Amer. Math. Soc. 312 (1989), 129-140
MSC: Primary 53C42; Secondary 57R40
DOI: https://doi.org/10.1090/S0002-9947-1989-0956030-4
MathSciNet review: 956030
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Abstract: We classify, locally and globally, the ruled Weingarten hypersurfaces of the Euclidean space. As a consequence of the local classification and a rigidity theorem of Dajczer and Gromoll, it follows that a complete Weingarten hypersurface which does not contain an open subset of the form $ {L^3} \times {{\mathbf{R}}^{n - 3}}$, where $ {L^3}$ is unbounded and $ n \geq 3$, is rigid.


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DOI: https://doi.org/10.1090/S0002-9947-1989-0956030-4
Article copyright: © Copyright 1989 American Mathematical Society