A NOTE ON SCALAR CURVATURE FUNCTIONS OF ALMOST-KÄAHLER METRICS
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We present a 4-dimensional nil-manifold as the first example of a closed non-Kählerian symplectic manifold with the following property: a function is the scalar curvature of some almost Kähler metric iff it is negative somewhere. This is motivated by the Kazdan-Warner's work on classifying smooth closed manifolds according to the possible scalar curvature functions.
Abstract
We present a 4-dimensional nil-manifold as the first example of a closed non-Kählerian symplectic manifold with the following property: a function is the scalar curvature of some almost Kähler metric iff it is negative somewhere. This is motivated by the Kazdan-Warner's work on classifying smooth closed manifolds according to the possible scalar curvature functions.
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