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Self-duality and differentiable structures on the connected sum of complex projective planes. (English) Zbl 0808.32028
The authors prove that if the twistor space of a 4-dimensional simply connected self-dual manifold \(M\) of positive scalar curvature admits a real effective divisor of degree 2, then \(M\) is diffeomorphic to a connected sum \(nP_ 2 (C)\) for some \(n\). In particular, it follows that if a self-dual manifold \(M\) of positive scalar curvature is homeomorphic to \(4P_ 2 (C)\), then \(M\) is diffeomorphic to \(4P_ 2 (C)\).
Reviewer: K.Ogiue (Tokyo)

MSC:
32L25 Twistor theory, double fibrations (complex-analytic aspects)
53A30 Conformal differential geometry (MSC2010)
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
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