Dupin子流形的约化
Reducibility of Dupin submanifolds
摘要：
本文对具有任意余维的Dupin子流形引入了弱可约性的概念。我们给出了所有弱可约Dupin子流形的一个完整的特征，作为一个更广泛的一类欧氏子流形的一般结果的后果。作为一个主要应用，我们给出了一个显式的递归方法，利用一阶线性偏微分方程的完全可积系统的解生成所有完整Dupin子流形.得到了关于Dupin子流形的几个新结果。
英文摘要：
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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