**Journal of Lie Theory
**

Vol. 8, No. 2, pp. 279-292 (1998)

#
On solvmanifolds and a conjecture of Benson and Gordon from the hamiltonian viewpoint

##
A. Tralle and W. Andrzejewski

Aleksy Tralle

Institute of Mathematics

University of Wroclaw

Plac Grunwaldzki 2/4, 50-384 Wroclaw,

Poland

tralle@math.uni.wroc.pl
Wojciech Andrzejewski

Institute of Mathematics

University of Szczecin

Wielkopolska 15, 70-451 Szczecin

Poland

**Abstract:** In this work we prove a theorem which shows that under some mild restrictions on a solvmanifold $\scriptstyle G/\Gamma$ the existence of a Kähler structure on it forces $\scriptstyle G$ to be metabelian and, hence this result is only `one-step' removed from the original Benson-Gordon conjecture. Applications and examples are discussed. The proof develops the `hamiltonian' idea of D. McDuff which appeared in her proof of the same conjecture for nilmanifolds [22] as well as ideas of G. Lupton and J. Oprea contained in [20].

**Full text of the article:**

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