Osaka Journal of Mathematics

A note on compact solvmanifolds with Kähler structures

Keizo Hasegawa

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In this note we show that a compact solvmanifold admits a Kähler 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 Kähler structure if and only if it is a complex torus, which is known as the Benson-Gordon's conjecture.

Article information

Osaka J. Math., Volume 43, Number 1 (2006), 131-135.

First available in Project Euclid: 28 April 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32Q15: Kähler manifolds 32M10: Homogeneous complex manifolds [See also 14M17, 57T15]
Secondary: 53C30: Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15] 53D05: Symplectic manifolds, general


Hasegawa, Keizo. A note on compact solvmanifolds with Kähler structures. Osaka J. Math. 43 (2006), no. 1, 131--135.

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