Abstract
We first present a new proof of a result of Calabi, nonnegativeness of the Hessian of the Calabi functional at an extremal Kähler metric. Then we extend the result to the general context of a reductive group action on a Kähler manifold admitting a moment map. Precisely, we show nonnegativeness of the Hessian of the norm function along a complex orbit at a critical point.
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Mathematics Subject Classification (1991): Primary 53C55; Secondary 53D20, 58E11
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Wang, L. Hessians of the Calabi Functional and the Norm Function. Ann Glob Anal Geom 29, 187–196 (2006). https://doi.org/10.1007/s10455-005-9014-4
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DOI: https://doi.org/10.1007/s10455-005-9014-4