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- Title
The Ricci pinching functional on solvmanifolds.
- Authors
Lauret, Jorge; Will, Cynthia E
- Abstract
We study the natural functional |$F=\frac {\operatorname {scal}^2}{|\operatorname {Ric}|^2}$| on the space of all non-flat left-invariant metrics on all solvable Lie groups of a given dimension |$n$|. As an application of properties of the beta operator, we obtain that solvsolitons are the only global maxima of |$F$| restricted to the set of all left-invariant metrics on a given unimodular solvable Lie group, and beyond the unimodular case, we obtain the same result for almost-abelian Lie groups. Many other aspects of the behavior of |$F$| are clarified.
- Subjects
SOLVABLE groups; LIE groups; INVARIANT sets
- Publication
Quarterly Journal of Mathematics, 2019, Vol 70, Issue 4, p1281
- ISSN
0033-5606
- Publication type
Article
- DOI
10.1093/qmath/haz020