Abelian para-Kaehler structures on Lie algebras
Para-Kaehler Lie algebras which decompose as the sum of two abelian Lagrangian subalgebras are studied. We propose several constructions and provide an inductive description of such Lie algebras. The curvatures of the para-Kaehler metric are computed and sufficient conditions to ensure flatness or R...
Saved in:
Published in | Differential geometry and its applications Vol. 29; no. 2; pp. 160 - 173 |
---|---|
Main Authors | , |
Format | Journal Article |
Language | English |
Published |
01.01.2011
|
Subjects | |
Online Access | Get full text |
Cover
Loading…
Summary: | Para-Kaehler Lie algebras which decompose as the sum of two abelian Lagrangian subalgebras are studied. We propose several constructions and provide an inductive description of such Lie algebras. The curvatures of the para-Kaehler metric are computed and sufficient conditions to ensure flatness or Ricci-flatness are given. The Lie algebras for which the para-Kaehler metric is Einstein and non-Ricci-flat are completely characterized. |
---|---|
Bibliography: | ObjectType-Article-2 SourceType-Scholarly Journals-1 content type line 23 ObjectType-Feature-1 |
ISSN: | 0926-2245 |
DOI: | 10.1016/j.difgeo.2011.02.003 |