Reducibility of Dupin submanifolds

Details Reducibility of Dupin submanifolds Reducibility of Dupin submanifolds

2004-03-24

arxiv.org/abs/math/0403418v1

Mathematics

Differential Geometry

32 pages

Scientific paper

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.

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