Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

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


Author: Brian Weber
Journal: Proc. Amer. Math. Soc. 147 (2019), 3117-3130
MSC (2010): Primary 53C26, 53C24; Secondary 58J60
DOI: https://doi.org/10.1090/proc/14014
Published electronically: April 3, 2019
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 53C26, 53C24, 58J60

Retrieve articles in all journals with MSC (2010): 53C26, 53C24, 58J60


Additional Information

Brian Weber
Affiliation: Department of Mathematics, University of Pennsylvania, 209 South 33rd Street, Philadelphia, Pennsylvania 19104-6395
Email: brianwebermathematics@gmail.com

DOI: https://doi.org/10.1090/proc/14014
Keywords: Ricci-flat manifolds, 4-manifolds, Killing fields
Received by editor(s): September 19, 2017
Published electronically: April 3, 2019
Communicated by: Lei Ni
Article copyright: © Copyright 2019 American Mathematical Society