A note on tame/compatible almost complex structures on four-dimensional Lie algebras

Abstract

Four-dimensional, oriented Lie algebras $\mathfrak{g}$ which satisfy the tame-compatible question of Donaldson for all almost complex structures $J$ on $\mathfrak{g}$ are completely described. As a consequence, examples are given of (non-unimodular) four-dimensional Lie algebras with almost complex structures which are tamed but not compatible with symplectic forms.

12 pages

References in corpus (7)

• Taming symplectic forms and the Calabi-Yau equation
• On Cohomological Decomposition of Almost-Complex Manifolds and Deformations
• Almost Kähler structures on four dimensional unimodular Lie algebras
• The Calabi-Yau equation on the Kodaira-Thurston manifold
• Almost Kahler forms on rational 4-manifolds
• Hyper-Kähler quotients of solvable Lie groups
• Tamed symplectic structures on compact solvmanifolds of completely solvable type