I would also like to mention an interesting related result of T. Fujita (which is not cited in the referenced survey article). "On topological characterizations of complex projective spaces and affine linear spaces", Proc. Japan Acad. Ser. A Math. Sci. 56 (1980), no. 5, 231–234.
Theorem: Let X be a smooth Fano n-fold with cohomology ring isomorphic to $\mathbb{CP}^n$ and $n \leq 5$. Then $X \cong \mathbb{CP}^n$.