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arXiv · 1709.10342

On Ricci negative solvmanifolds and their nilradicals

Jonas Deré·Jorge Lauret
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Abstract

In the homogeneous case, the only curvature behavior which is still far from being understood is Ricci negative. In this paper, we study which nilpotent Lie algebras admit a Ricci negative solvable extension. Different unexpected behaviors were found. On the other hand, given a nilpotent Lie algebra, we consider the space of all the derivations such that the corresponding solvable extension has a metric with negative Ricci curvature. Using the nice convexity properties of the moment map for the variety of nilpotent Lie algebras, we obtain a useful characterization of such derivations and some applications.

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Jonas Deré, Jorge Lauret. 2017-09-29. On Ricci negative solvmanifolds and their nilradicals. https://arxiv.org/abs/1709.10342

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