There are many classification theorems for hypersurfaces M 2n−1 in the complex projective space CP n and the complex hyperbolic space CHn . The most prominent model spaces are the homogeneous Hopf hypersurfaces catalogued by R. Takagi for CP n and S. Montiel for CHn . The case n = 2 has proven to be more challenging than the higher dimensional ones. For example, all pseudo-Einstein hypersurfaces are known to belong the the lists of Takagi or Montiel when n ≥ 3, but not for n = 2. We will discuss this and other results involving contractions of the curvature tensor, with emphasis on how CP 2 and CH2 differ from the n ≥ 3 case.