Curved flats in symmetric spaces (Q1353040)

The authors introduce a new class of so-called curvature flat submanifolds, i.e., submanifolds of symmetric spaces defined by the property that the curvature tensor of the ambient space vanishes on them. These submanifolds are analogous to the developable surfaces in \(\mathbb{R}^3\), but they generalize other concepts such as isometric immersions, conformally flat subspaces, and isothermic surfaces. Starting with the Lie algebra definition, general properties of the concept are investigated, and the integration of the fundamental curved flat equations involving an additional ``spectral'' parameter is replaced by a hierarchy of finite-dimensional commuting ordinary differential equations in the Lax form.