The structure Jacobi operator for hypersurfaces in CP^2 and CH^2
  Using the methods of moving frames, we study real hypersurfaces in complex projective space CP^2 and complex hyperbolic space CH^2 whose structure Jacobi operator has various special properties. Our results complement work of several other authors who worked on such hypersurfaces in CP^n and CH^n for n>2. 
Thomas A. Ivey, Patrick J. Ryan