A critical metric for the $L^2$-norm of the curvature tensor on $S^3$
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- by François Lamontagne PDF
- Proc. Amer. Math. Soc. 126 (1998), 589-593 Request permission
Abstract:
The $L^2$-norm of the curvature tensor \[ \mathcal {R}(g)=\frac {1}{(\mathrm {Vol}(M))^{\frac {n-4}{n}}}\int _{M}\mid R \mid ^{2}dvol_{g} \] defines a Riemannian functional on the space of metrics. This work exhibits a metric on $S^3$ which is of Berger type but not of constant ricci curvature, and yet is critical for $\mathcal {R}$.References
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Additional Information
- François Lamontagne
- Affiliation: Centre de Recherches Mathématiques, Université de Montréal, Montréal, Québec, Canada
- Email: lamontaf@crm.umontreal.ca
- Received by editor(s): December 7, 1995
- Received by editor(s) in revised form: July 31, 1996
- Communicated by: Christopher Croke
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 589-593
- DOI: https://doi.org/10.1090/S0002-9939-98-04171-9
- MathSciNet review: 1425130