A note on higher extremal metrics
Differential Geometry
2017-09-29 v2
Abstract
In this paper we introduce higher extremal Kahler 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 a formula due to Liu for the Bando-Futaki invariants (which are obstructions for the existence of harmonic Chern forms) of hypersurfaces in projective space.
Cite
@article{arxiv.1607.05907,
title = {A note on higher extremal metrics},
author = {Vamsi Pritham Pingali},
journal= {arXiv preprint arXiv:1607.05907},
year = {2017}
}
Comments
Minor typographical changes. To appear in the transactions of the american mathematical society