Equifocal families in symmetric spaces of compact type
  An equifocal submanifold M of a symmetric space N of compact type induces a foliation with singular leaves on N. In this paper we will show how to reconstruct the equifocal foliation starting from one of the singular leaves, the so-called focal manifolds. To be more concrete: The equifocal submanifold is equal to a partial tube B around the focal manifold and we will show how to construct B in this paper. Moreover, we will find a geometrical characterization of focal manifolds. 
Martina Brueck