Geodesic
Extremal Kähler metrics and Hamiltonian functions II
Glasgow mathematical journal, Tome 44 (2002) no. 2, pp. 241-253

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We apply a previously obtained ansatz for extremal Kähler metrics to show that if a manifold admits a Hodge metric with constant scalar curvature, then the total space of the projectivization of a line bundle with first Chern class equal to the Kähler class of the metric admits a one-parameter family of extremal Kähler metrics. This generalizes earlier constructions. 
Tønnesen-Friedman, Christina W. Extremal Kähler metrics and Hamiltonian functions II. Glasgow mathematical journal, Tome 44 (2002) no. 2, pp. 241-253. doi: 10.1017/S0017089502020050
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     title = {Extremal {K\"ahler} metrics and {Hamiltonian} functions {II}},
     journal = {Glasgow mathematical journal},
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     year = {2002},
     volume = {44},
     number = {2},
     doi = {10.1017/S0017089502020050},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089502020050/}
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