## 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.## References

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## Additional Information

**Vamsi Pritham Pingali**- Affiliation: Department of Mathematics, Indian Institute of Science, Bangalore, India - 560012
- Email: vamsipingali@iisc.ac.in
- Received by editor(s): February 15, 2017
- Published electronically: April 4, 2018
- Additional Notes: The author was supported by SERB grant No. ECR/2016/001356 and also thanks the Infosys foundation for the Infosys Young Investigator Award.
- © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**370**(2018), 6995-7010 - MSC (2010): Primary 53C25, 53C55
- DOI: https://doi.org/10.1090/tran/7416
- MathSciNet review: 3841840