On Hermitian surfaces with \(J\)-invariant Ricci tensor
Let \(M(J,g)\) be a compact Hermitian surface. Let \(s\) denote the usual scalar curvature of \(M(J,g)\), and \(k\) its conformal scalar curvature. By definition, \(k\) is the scalar curvature with respect to \(g\) of the canonical Weyl structure associated to the Hermitian structure \((J,g)\). The main result states that if the Ricci tensor of \(g\) is \(J\)-invariant and the difference \(s-k\) is constant, then \(M(J,g)\) must be Kähler.
scientific article; zbMATH DE number 1760632