Blaschke's problem for hypersurfaces

2006/08/02 by Marcos Dajczer, Ruy Tojeiro, Dajczer, Marcos +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.math/0608065

openalex publication_date 2006/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We solve Blaschke's problem for hypersurfaces of dimension n≥ 3. Namely, we determine all pairs of Euclidean hypersurfaces f,f\colon Mⁿ→\Rⁿ⁺¹ that induce conformal metrics on Mⁿ and envelope a common sphere congruence in \Rⁿ⁺¹.

Citations

• Conformal de Rham decomposition of Riemannian manifolds

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