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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Energy and asymptotics of Ricci-flat 4-manifolds with a Killing field
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by Brian Weber PDF
Proc. Amer. Math. Soc. 147 (2019), 3117-3130 Request permission

Abstract:

If a complete 4-manifold with $\operatorname {Ric}=0$ has a nowhere zero Killing field, we prove it is flat, generalizing a classic result on compact manifolds. If the Killing field has compact zero-locus, we compute the manifold’s $L^2$-energy.
References
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Additional Information
  • Brian Weber
  • Affiliation: Department of Mathematics, University of Pennsylvania, 209 South 33rd Street, Philadelphia, Pennsylvania 19104-6395
  • MR Author ID: 710322
  • Email: brianwebermathematics@gmail.com
  • Received by editor(s): September 19, 2017
  • Published electronically: April 3, 2019
  • Communicated by: Lei Ni
  • © Copyright 2019 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 3117-3130
  • MSC (2010): Primary 53C26, 53C24; Secondary 58J60
  • DOI: https://doi.org/10.1090/proc/14014
  • MathSciNet review: 3973911