The Ricci pinching functional on solvmanifolds
Differential Geometry
2019-05-13 v2
Abstract
We study the natural functional F=scal^2/|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.
Keywords
Cite
@article{arxiv.1808.01380,
title = {The Ricci pinching functional on solvmanifolds},
author = {Jorge Lauret and Cynthia E. Will},
journal= {arXiv preprint arXiv:1808.01380},
year = {2019}
}
Comments
21 pages. Final version to appear in Quart. J. Math