Abstract
We give some explicit examples of compact Kählerian solvmanifolds and, by extending them naturally, we find a class of compact Kählerian solvmanifolds; namely, a finite quotient of a complex torus that is a holomorphic fiber bundle over a complex torus with fiber a complex torus. Then we see that under some restriction a compact solvmanifold is Kählerian if and only if it belongs to this class. We are thus led to a conjecture that this result would hold without any restriction.
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Hasegawa, K. A Class of Compact Kählerian Solvmanifolds and a General Conjecture. Geometriae Dedicata 78, 253–258 (1999). https://doi.org/10.1023/A:1005222228809
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DOI: https://doi.org/10.1023/A:1005222228809