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Extremal Kähler metrics and Hamiltonian functions

Thierry Chave - No affiliation found

1999/08/01 Full-length article DOI: 10.1016/S0393-0440(98)00069-2 Journal: Journal of Geometry and Physics

Abstract:

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.