Non-K\"ahler complex structures on $R^4$

Antonio J. Di Scala; Daniele Zuddas; Naohiko Kasuya

arxiv: 1501.06097 · v4 · pith:P7TWTQHJnew · submitted 2015-01-24 · 🧮 math.GT · math.AG· math.CV· math.DG· math.SG

Non-K\"ahler complex structures on R⁴

Antonio J. Di Scala , Naohiko Kasuya , Daniele Zuddas This is my paper

classification 🧮 math.GT math.AGmath.CVmath.DGmath.SG

keywords complexstructuresahlercalabieckmannnon-kanalogiesconstruct

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We construct the first examples of non-K\"ahler complex structures on $R^4$. These complex surfaces have some analogies with the complex structures constructed in early Fifties by Calabi and Eckmann on the products of two odd-dimensional spheres. However, our construction is quite different from that of Calabi and Eckmann.

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Non-K\"ahler complex structures on R⁴

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