English

A complete solution of Samuel's problem

Differential Geometry 2010-04-02 v1

Abstract

We give a complete solution of a problem in submanifold theory posed and partially solved by the eminent algebraic geometer Pierre Samuel in 1947. Namely, to determine all pairs of immersions of a given manifold into Euclidean space that have the same Gauss map and induce conformal metrics on the manifold. The case of isometric induced metrics was solved in 1985 by the first author and D. Gromoll.

Cite

@article{arxiv.1004.0142,
  title  = {A complete solution of Samuel's problem},
  author = {Marcos Dajczer and Ruy Tojeiro},
  journal= {arXiv preprint arXiv:1004.0142},
  year   = {2010}
}

Comments

28 pages

R2 v1 2026-06-21T15:05:31.319Z