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Uniqueness of the complex structure on Kähler manifolds of certain homotopy types. (English) Zbl 0711.53052
The main result of this paper is that for $$n\leq 6$$, a Kähler manifold which is homotopy equivalent to the projective space $${\mathbb{C}}{\mathbb{P}}_ n$$ is analytically equivalent to $${\mathbb{C}}{\mathbb{P}}_ n$$. An ad hoc proof is given for each of the cases $$n=3,4,5,6$$.
Reviewer: G.Roos

##### MSC:
 53C55 Global differential geometry of Hermitian and Kählerian manifolds 57R20 Characteristic classes and numbers in differential topology 57R55 Differentiable structures in differential topology
##### Keywords:
complex projective spaces; homotopy type; Kähler manifold
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