On Einstein extensions of nilpotent metric Lie algebras

被引：0
作者：
Yu. G. Nikonorov
机构：
[1] Rubtsovsk Industrial Institute,
来源：
Siberian Advances in Mathematics | 2007年 / 17卷 / 3期
关键词：
Einstein metrics; Riemannian manifolds; nilpotent metric Lie algebras; solvmanifolds;
D O I：
10.3103/S1055134407030017
中图分类号：
学科分类号：
摘要：
The main result of the article is as follows: If a nilpotent noncommutative metric Lie algebra (n, Q) is such that the operator Id − trace(Ric) / trace(Ric2) Ric is positive definite then every Einstein solvable extension of (n, Q) is standard. We deduce several consequences of this assertion. In particular, we prove that all Einstein solvmanifolds of dimension at most 7 are standard.
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页码：153 / 170
页数：17
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