Transformations on harmonic maps and Willmore surfaces

• Applicant: Professorin Dr. Katrin Leschke
• Subject Area: Mathematics
• Term: from 2007 to 2010
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 43065796

Various surface classes which are described by curvature properties are given as critical points of variational problems: examples include the critical points of the area functional under prescribed volume, the so-called constant mean curvature surfaces (CMC), and the critical points of the bending energy, the so-called Willmore surfaces. Transformations which preserve special surface classes play an important role in surface theory: originally used to construct new, more complicated examples from simple ones, they are recently also linked to complete integrability and whence can be used for classification purposes.The case of CMC and Willmore surfaces is well known to be related to the theory of harmonic maps into symmetric spaces. We propose to study generalizations of the classical Darboux and Bäcklund transformation to general harmonic maps. Results for these transformations will have interesting applications to special surface classes such as Willmore surfaces and Hamiltonian Stationary Lagrangian surfaces.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1154: Global Differential Geometry