Rigidity and infinitesimal deformability of Ricci solitons
  In this paper, an obstruction against the integrability of certain infinitesimal solitonic deformations is given. Using this obstruction, we show that the complex projective spaces of even complex dimension are rigid as Ricci solitons although they have infinitesimal solitonic deformations. 
Klaus Kroencke
math.DG