Abstract
In this note we show that a compact solvmanifold admits a Kahler structure if and only if it is a finite quotient of a complex torus which has a structure of a complex torus bundle over a complex torus. We can show in particular that a compact solvmanifold of completely solvable type has a Kahler structure if and only if it is a complex torus, which is known as the Benson-Gordon's conjecture.
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