Abstract
We build examples of Norden metrics on Σ × S 1, where Σ ⊂ R 2 n n is either a pseudosphere or a pseudohyperbolic space. These turn out to be locally conformal to flat anti-Kählerian metrics, strongly non anti-Kählerian, 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 × S 1.
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Dragomir, S., Francaviglia, M. On Norden Metrics which Are Locally Conformal to Anti-Kählerian Metrics. Acta Applicandae Mathematicae 60, 115–135 (2000). https://doi.org/10.1023/A:1006354630911
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DOI: https://doi.org/10.1023/A:1006354630911