Time-like isothermic surfaces associated to Grassmannian systems (Q2576621)

\textit{C.-L.~Terng} introduced in [J. Differ. Geom. 45, 407--445 (1997; Zbl 0877.53022)] a new class of integrable systems involving a symmetric space \(U/K\) and a maximal abelian subalgebra of \({\mathfrak p}\) in a Cartan decomposition \({\mathfrak u} = {\mathfrak k} + {\mathfrak p}\) of the Lie algebra of \({\mathfrak u}\). One of the basic problems in this context is to understand the geometry of a given \(U/K\)-system. In the present paper the authors show that the \(U/K\)-systems associated to the symmetric space \(O(n-j+1,j+1)/O(n-j,j) \times O(1,1)\) and two particular choices of inequivalent maximal abelian subalgebras lead to the geometry of time-like isothermic surfaces in the pseudo-Riemannian space \({\mathbb R}^{n-j,j}\).