Reducibility of Dupin submanifolds

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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.
32 pages

Keywords

Differential Geometry, 53B25

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/70578

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0403418
 http://arxiv.org/abs/math/0403418

Collections

arXiv