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Blaschke's problem for hypersurfaces

Marcos Dajczer·Ruy Tojeiro
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Abstract

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

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Marcos Dajczer, Ruy Tojeiro. 2006-08-02. Blaschke's problem for hypersurfaces. https://arxiv.org/abs/math/0608065

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