A note on higher extremal metrics

Pingali, Vamsi

doi:10.1090/tran/7416

A note on higher extremal metrics
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by Vamsi Pritham Pingali PDF

Trans. Amer. Math. Soc. 370 (2018), 6995-7010 Request permission

Abstract:

In this paper we introduce “higher extremal Kähler” metrics. We provide an example of the same on a minimal ruled surface. We also prove a perturbation result that implies that there are non-trivial examples of “higher constant scalar curvature” metrics, which are basically metrics where the top Chern form is harmonic. We also give a relatively short proof of Liu’s formula for the Bando-Futaki invariants (which are obstructions for the existence of harmonic Chern forms) of hypersurfaces of projective space.

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