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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

A note on higher extremal metrics


Author: Vamsi Pritham Pingali
Journal: Trans. Amer. Math. Soc. 370 (2018), 6995-7010
MSC (2010): Primary 53C25, 53C55
DOI: https://doi.org/10.1090/tran/7416
Published electronically: April 4, 2018
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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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Additional Information

Vamsi Pritham Pingali
Affiliation: Department of Mathematics, Indian Institute of Science, Bangalore, India - 560012
Email: vamsipingali@iisc.ac.in

DOI: https://doi.org/10.1090/tran/7416
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.
Article copyright: © Copyright 2018 American Mathematical Society

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