Vaisman manifolds with large b1 and c1^b=0 are diffeomorphic to Kodaira-Thurston manifolds with left-invariant complex structure and regular foliation.
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On the Classification of Vaisman Manifolds with Vanishing First Basic Chern Class and Large First Betti Number
Vaisman manifolds with large b1 and c1^b=0 are diffeomorphic to Kodaira-Thurston manifolds with left-invariant complex structure and regular foliation.