Rigidity for complete Weingarten hypersurfaces

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.