Concerning the existence of Einstein and Ricci soliton metrics on solvable Lie groups

被引:21
作者
Jablonski, Michael [1 ]
机构
[1] Univ Oklahoma, Dept Math, Norman, OK 73019 USA
关键词
ALGEBRAIC-GROUPS; MOMENT MAP; SOLVMANIFOLDS; NILMANIFOLDS; ORBITS;
D O I
10.2140/gt.2011.15.735
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this work we investigate solvable and nilpotent Lie groups with special metrics. The metrics of interest are left-invariant Einstein and algebraic Ricci soliton metrics. Our main result shows that one may determine the existence of a such a metric by analyzing algebraic properties of the Lie algebra and infinitesimal deformations of any initial metric. Our second main result concerns the isometry groups of such distinguished metrics. Among the completely solvable unimodular Lie groups (this includes nilpotent groups), if the Lie group admits such a metric, we show that the isometry group of this special metric is maximal among all isometry groups of left-invariant metrics.
引用
收藏
页码:735 / 764
页数:30
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