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Locally conformally flat Kähler and para-Kähler manifolds. (English) Zbl 1469.53070

Let \((M,g,J_\epsilon)\) be a (para-)Kähler manifold, where \(J_\epsilon\) denotes the parallel (para-)complex structure, \(J_\epsilon^2 =-\epsilon \operatorname{Id}\) and \(g(J_\epsilon X,J_\epsilon Y) =\epsilon g(X,Y)\) for \(\epsilon =\pm 1\). The authors complete the classification of locally conformally flat Kähler and para-Kähler manifolds, describing all possible non-flat curvature models for Kähler and para-Kähler surfaces.

MSC:

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53B35 Local differential geometry of Hermitian and Kählerian structures
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
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