Examples of Hermitian manifolds with pointwise constant anti-holomorphic sectional curvature (Q1882457)

Let \((M,J,g)\) be an almost Hermitian manifold. It is said to have pointwise constant anti-holomorphic sectional curvature if the sectional curvature \(K_p(\alpha)\) of a totally real 2-plane~\(\alpha\) at the point \(p\in M\) only depends on~\(p\) and not on the choice of the totally real 2-plane~\(\alpha\). In this paper, the author describes a method for constructing non-compact examples of Hermitian manifolds of this type. They are obtained by making a suitable conformal change of the metric on (an open set of) a complex space form. All explicitly given new examples are four-dimensional.