等温曲面：共形几何，Clifford代数和可积系统
Isothermic surfaces: conformal geometry, Clifford algebras and integrable systems
摘要：
我们给出了一个帐户的经典和可积几何的等温表面在任意余维。我们表明，经典的转换理论的达布，比安奇和Calapso通过在任意的余维不变的连接与“弯曲的单位”的Ferus和Pedit。此外，我们还将达布变换与Terng和Uhlenbeck意义下的“简单因子”的修饰作用等同起来。在这样做，我们宣传使用Vahlen的Clifford代数矩阵作为一个有效的计算工具，在共形几何。
英文摘要：
We give an account of the classical and integrable geometry of isothermic surfaces in arbitrary co-dimension. We show that the classical transformation theory of Darboux, Bianchi and Calapso goes through unchanged in arbitrary co-dimension as does the connection with the "curved flats" of Ferus and Pedit. Moreover, we identify Darboux transformations with the dressing action of "simple factors" in the sense of Terng and Uhlenbeck. In so doing, we advertise the use of Vahlen's Clifford algebra matrices as an efficient computational tool in conformal geometry.
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