Geometriae Dedicata

, Volume 125, Issue 1, pp 93–101 | Cite as

Locally conformal Kähler structures on compact nilmanifolds with left-invariant complex structures

Original Paper


Let (M, g, J) be a compact Hermitian manifold and \(\Omega\) the fundamental 2-form of (g, J). A Hermitian manifold (M, g, J) is called a locally conformal Kähler manifold if there exists a closed 1-form α such that \(d\Omega=\alpha \wedge \Omega\) . The purpose of this paper is to give a completely classification of locally conformal Kähler nilmanifolds with left-invariant complex structures.


Locally conformal Kähler structure Nilmanifold 

Mathematics Subject Classifications (2000)

primary 53C55 secondary 17B30 


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Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  1. 1.Department of MathematicsOsaka UniversityToyonaka, OsakaJapan

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