Mathematics – Differential Geometry
Scientific paper
2010-04-21
Mathematics
Differential Geometry
11 pages. typos and quotations corrected.
Scientific paper
Given a path of almost-K\"ahler metrics compatible with a fixed symplectic form on a compact 4-manifold such that at time zero the almost-K\"ahler metric is an extremal K\"ahler one, we prove, for a short time and under a certain hypothesis, the existence of a smooth family of extremal almost-K\"ahler metrics compatible with the same symplectic form, such that at each time the induced almost-complex structure is diffeomorphic to the one induced by the path.
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