English

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.

Keywords

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

R2 v1 2026-06-22T14:59:20.519Z