Energy and asymptotics of Ricci-flat 4-manifolds with a Killing field
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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