On Norden Metrics which Are Locally Conformal to Anti-Kählerian Metrics

Abstract

We build examples of Norden metrics on Σ × S1, where Σ ⊂ R2 nn is either a pseudosphere or a pseudohyperbolic space. These turn out to be locally conformal to flat anti-Kahlerian metrics, strongly non anti-Kahlerian, and with a parallel Lee form. Conversely, any connected complete anti-Hermitian manifold possessing these properties is shown to be locally analytically homothetic to Σ × S1.