Abstract
We solve Blaschke’s problem for hypersurfaces of dimension \(n \geq 3\) . 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 envelop a common sphere congruence in \(\mathbb{R}^{n+1}\) .
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