论文标题
关于RICCI负面推导
On Ricci negative derivations
论文作者
论文摘要
鉴于nilpotent lie代数，我们研究了所有可对角线衍生的衍生物的空间，以使相应的一维溶解延伸范围允许左ricci曲率负左右不变的度量标准。 Lauret-Will猜想这样的空间与开放式和凸的子集相吻合，该子集的定义是根据MONT MAP的各种nilpotent Lie代数代数的。我们证明了猜想在维度5以及海森堡和标准丝状谎言代数中的有效性。
Given a nilpotent Lie algebra, we study the space of all diagonalizable derivations such that the corresponding one-dimensional solvable extension admits a left-invariant metric with negative Ricci curvature. It has been conjectured by Lauret-Will that such a space coincides with an open and convex subset of derivations defined in terms of the moment map for the variety of nilpotent Lie algebras. We prove the validity of the conjecture in dimension 5, as well as for Heisenberg and standard filiform Lie algebras.
