My  apology  in advance if this  question is obvious:

I  know that an  Einstein manifold  need  not  have  a  constant  sectional  curvature  example $\mathbb{C}P^n$.  But  this  space  has a  constant holomorphic sectional  curvature.

What  Einstein  manifold admit  a  holomorphic  structure whose  holomorphic  sectional  curvature is  not  constant?


**Note:**  I  admit that I  do not know the  answer  to the  above  question.  But after that I  know  an  answer the  next  step  would  be the  following: What is  a  manifold who  admite  Einstein  structure  and  also  holomorphic  structure  but  does  not  admit simultaneously  a  Riemannian metric  and  a  holomorphic  structure for  which the holomorphic  sectional  curvature would be  constant.  However  I  do  not include this  question to this post as original main question. Because I do not know even its  elementary  version, i.e, the main question.