Orateur
Description
In classical differential geometry, geometric transformations have been used to create new curves and surfaces from simple ones: the aim is to solve the underlying defining compatibility equations of curve or surface classes by finding solutions to a simpler system of differential equations arising from the transforms. Classically, the main concern was a local theory. In modern theory, global questions have led to a renewed interest in classical transformations. For example, in the case of a torus, the investigation of closing conditions for Darboux transforms naturally leads to the notion of the spectral curve of the torus. In this talk we discuss closing conditions for smooth and discrete polarised curves, isothermic surfaces and CMC surfaces. In particular, we obtain new explicit periodic discrete polarised curves, new discrete isothermic tori and new explicit smooth CMC cylinder.
