Blaschke's problem for hypersurfaces

Abstract

We solve Blaschke's problem for hypersurfaces of dimension $n\ge 3$. Namely, we determine all pairs of Euclidean hypersurfaces $f,\tilde{f}:M^n\to {\mathbb{R}}^{n+1}$ that induce conformal metrics on $M^n$ and envelope a common sphere congruence in ${\mathbb{R}}^{n+1}$.

References in corpus (2)

• Conformal de Rham decomposition of Riemannian manifolds
• Exploring Surfaces through Methods from the Theory of Integrable Systems. lectures on the Bonnet problem