Negative eigenvalues of the Ricci operator of solvable metric Lie algebras

被引：0
作者：
Yu. G. Nikonorov
机构：
[1] South Mathematical Institute of Vladikavkaz Scientific Centre of the Russian Academy of Sciences,
来源：
Geometriae Dedicata | 2014年 / 170卷
关键词：
Left-invariant Riemannian metrics; Lie groups; Metric Lie algebras; Ricci operator; Eigenvalues of the Ricci operator; Ricci curvature; 53C30; 17B30;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper we get a necessary and sufficient condition for the Ricci operator of a solvable metric Lie algebra to have at least two negative eigenvalues. In particular, this condition implies that the Ricci operator of every non-unimodular solvable metric Lie algebra or every non-abelian nilpotent metric Lie algebra has this property.
引用
收藏
页码：119 / 133
页数：14
相关论文
共 13 条
[1]  
Abiev N.A.(2013)On the Ricci curvature of solvable metric Lie algebras with two-step nilpotent derived algebras Mat. tr. 16 3-18
[2]  
Chen D(2009)A note on Ricci signatures Proc. Am. Math. Soc. 137 273-278
[3]  
Dotti-Miatello I.(1982)Ricci curvature of left-invariant metrics on solvable unimodular Lie groups Math. Zeitschtift 180 257-263
[4]  
Glickenstein D(2010)Ricci flow on three-dimensional, unimodular metric Lie algebras Comm. Anal. Geom. 18 927-961
[5]  
Payne TL(1971)The scalar curvature of left invariant Riemannian metrics Indiana Univ. Math. J. 20 1125-1143
[6]  
Jensen G(2009)Ricci curvatures of left invariant Riemannian metrics on five dimensional nilpotent Lie groups Sib. Elektron. Mat. Izv. 6 326-339
[7]  
Kremlyov A.G.(2011)The Ricci flow for simply connected nilmanifolds Comm. Anal. Geom. 19 831-854
[8]  
Lauret J(1976)Curvatures of left invariant metrics on Lie groups Adv. Math. 21 293-329
[9]  
Milnor J(2012)Ricci operator of completely solvable metric Lie algebras Mat. tr. 15 146-158
[10]  
Nikonorov Yu.G.(2010)The Ricci flow for nilmanifolds J. Mod. Dyn. 4 65-90
12