English

Blaschke's problem for hypersurfaces

Differential Geometry 2007-05-23 v1

Abstract

We solve Blaschke's problem for hypersurfaces of dimension n3n\geq 3. Namely, we determine all pairs of Euclidean hypersurfaces f,f~ ⁣:MnRn+1f,\tilde{f}\colon M^n\to\R^{n+1} that induce conformal metrics on MnM^n and envelope a common sphere congruence in Rn+1\R^{n+1}.

Keywords

Cite

@article{arxiv.math/0608065,
  title  = {Blaschke's problem for hypersurfaces},
  author = {Marcos Dajczer and Ruy Tojeiro},
  journal= {arXiv preprint arXiv:math/0608065},
  year   = {2007}
}