Extremal almost-Kähler metrics

Details Extremal almost-Kähler metrics Extremal almost-Kähler metrics

2009-08-06

arxiv.org/abs/0908.0859v3

Mathematics

Differential Geometry

21 pages. to appear in IJM. typos and quotations corrected

Scientific paper

We generalize the notions of the Futaki invariant and extremal vector field of a compact K\"ahler manifold to the general almost-Kahler case and show the periodicity of the extremal vector field when the symplectic form represents an integral cohomology class modulo torsion. We also give an explicit formula of the hermitian scalar curvature in Darboux coordinates which allows us to obtain examples of non-integrable extremal almost-K\"ahler metrics saturating LeBrun's estimates.

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