Bohle, Christoph ; Leschke, Katrin ; Pedit, Franz ; Pinkall, Ulrich (2012)
We study the space of conformal immersions of a 2-torus into the 4-sphere. The moduli space of generalized Darboux transforms of such an immersed torus has the structure of a Riemann surface, the spectral curve. This Riemann surface arises as the zero locus of the determinant of a holomorphic family of Dirac type operators parameterized over the complexified dual torus. The kernel line bundle o...Isothermic submanifolds of symmetric R-spaces
Burstall, Francis E. ; Donaldson, Neil M. ; Pedit, Franz ; Pinkall, Ulrich (2011)
We extend the classical theory of isothermic surfaces in conformal 3-space, due to Bour, Christo¤el, Darboux, Bianchi and others, to the more general context of submanifolds of symmetric R-spaces with essentially no loss of integrable structure.