Rigidity of complete Euclidean hypersurfaces
A ruled hypersurface \(N^ n\) of the Euclidean space \({\mathbb{R}}^{n+1}\) is called a ruled strip if all rulings are complete Euclidean spaces. The main result of this paper is that any complete hypersurface \(N^ n\) of \({\mathbb{R}}^{n+1}\), \(n\geq 3\), which does not contain an open subset \(L^ 3\times {\mathbb{R}}^{n-3}\) with \(L^ 3\) unbounded admits nondiscrete isometric deformations only along ruled strips. This result extends a theorem of Sacksteder where N is assumed to be compact.
scientific article; zbMATH DE number 4092250