On the conjugacy of maximal unipotent subgroups of real semisimple Lie   groups
  The existence of closed orbits of real algebraic groups on real algebraic varieties is established. As an application, it is shown that if G is a real reductive linear group with Iwasawa decomposition G= KAN, then every unipotent subgroup of G is conjugate to a subgroup of N. 
Hassan Azad and Indranil Biswas
math.GR math.AG