Unique isometric immersion into hyperbolic space
The main result of the paper establishes sufficient conditions under which two isometric immersions \(f_ 1\), \(f_ 2\) of a connected, orientable Riemannian \(n\)-manifold into the \((n+1)\)-hyperbolic space \(H^{n+1}\) are equivalent up to an isometry \(\tau\) of \(H^{n+1}\), i.e., \(\tau f_ 2=f_ 1\). As in the classical corresponding case of isometric immersions into the \((n+1)\)-Euclidean space, the result is formulated in terms of the Gauss maps of \(f_ 1\) and \(f_ 2\). The author's approach relies on the general rigidity study for hypersurfaces in \(H^{n+1}\).
scientific article; zbMATH DE number 438925