English

Reducibility of Dupin submanifolds

Differential Geometry 2007-05-23 v1

Abstract

We introduce the notion of weak reduciblity for Dupin submanifolds with arbitrary codimension. We give a complete characterization of all weakly reducible Dupin submanifolds, as a consequence of a general result on a broader class of Euclidean submanifolds. As a main application, we derive an explicit recursive procedure to generate all holonomic Dupin submanifolds in terms of solutions of completely integrable systems of linear partial differential equations of first order. We obtain several additional results on Dupin submanifolds.

Keywords

Cite

@article{arxiv.math/0403418,
  title  = {Reducibility of Dupin submanifolds},
  author = {Marcos Dajczer and Luis A. Florit and Ruy Tojeiro},
  journal= {arXiv preprint arXiv:math/0403418},
  year   = {2007}
}

Comments

32 pages

R2 v1 2026-07-22T17:03:42.478Z