Extremal Kähler metrics and Hamiltonian functions
Review articleOpen access

AbstractAssuming a real torus acting on a Kähler manifold through holomorphic isometries, we obtain an ansatz for extremal Kähler metrics and we get new extremal metrics on some CP1-bundles over products of Kähler-Einstein manifolds of negative scalar curvature. We prove that one of the extremal metrics in four dimensions is locally conformally Einstein.

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