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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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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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