Let J be an almost complex structure on a 4-dimensional and unimodular Lie algebra g. We show that there exists a symplectic form taming J if and only if there is a symplectic form compatible with J. We also introduce groups and as the subgroups of the Chevalley–Eilenberg cohomology classes which can be represented by J-invariant, respectively J-anti-invariant, 2-forms on g. and we prove a cohomological J-decomposition theorem following Draˇghici et al. (2010) [12]: . We discover that tameness of J can be characterized in terms of the dimension of , just as in the complex surface case. We also describe the tamed and compatible symplectic cones. Finally, two applications to homogeneous J on 4-manifolds are obtained.

Almost Kähler structures on four dimensional unimodular Lie algebras / T.-J. Li; A.Tomassini. - In: JOURNAL OF GEOMETRY AND PHYSICS. - ISSN 0393-0440. - 62:7(2012), pp. 1714-1731. [10.1016/j.geomphys.2012.03.007]

Almost Kähler structures on four dimensional unimodular Lie algebras

TOMASSINI, Adriano
2012

Abstract

Let J be an almost complex structure on a 4-dimensional and unimodular Lie algebra g. We show that there exists a symplectic form taming J if and only if there is a symplectic form compatible with J. We also introduce groups and as the subgroups of the Chevalley–Eilenberg cohomology classes which can be represented by J-invariant, respectively J-anti-invariant, 2-forms on g. and we prove a cohomological J-decomposition theorem following Draˇghici et al. (2010) [12]: . We discover that tameness of J can be characterized in terms of the dimension of , just as in the complex surface case. We also describe the tamed and compatible symplectic cones. Finally, two applications to homogeneous J on 4-manifolds are obtained.
Almost Kähler structures on four dimensional unimodular Lie algebras / T.-J. Li; A.Tomassini. - In: JOURNAL OF GEOMETRY AND PHYSICS. - ISSN 0393-0440. - 62:7(2012), pp. 1714-1731. [10.1016/j.geomphys.2012.03.007]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11381/2563645
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