On Ricci negative solvmanifolds and their nilradicals

JONAS DERÉ ; JORGE LAURET

MATHEMATISCHE NACHRICHTEN

WILEY-V C H VERLAG GMBH

Lugar: Weinheim; Año: 2019 vol. 292 p. 1462 - 1481

0025-584X

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.