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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.
Acta Applicandae Mathematicae – Springer Journals
Published: Sep 30, 2004
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