Isoparametric submanifolds in two-dimensional complex space forms
  We show that an isoparametric submanifold of a complex hyperbolic plane, according to the definition of Heintze, Liu and Olmos', is an open part of a principal orbit of a polar action. We also show that there exists a non-isoparametric submanifold of the complex hyperbolic plane that is isoparametric according to the definition of Terng's. Finally, we classify Terng-isoparametric submanifolds of two-dimensional complex space forms. 
Jose Carlos Diaz-Ramos, Miguel Dominguez-Vazquez, Cristina   Vidal-Casti\~neira
math.DG