Artículo
Anti-Kählerian geometry on Lie groups
Fecha de publicación:
06/03/2018
Editorial:
Springer
Revista:
Mathematical Physics, Analysis And Geometry
ISSN:
1385-0172
e-ISSN:
1572-9656
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
Let G be a Lie group of even dimension and let (g,J) be a left invariant anti-Kähler structure on G. In this article we study anti-Kähler structures considering the distinguished cases where the complex structure J is abelian or bi-invariant. We find that if G admits a left invariant anti-Kähler structure (g,J) where J is abelian then the Lie algebra of G is unimodular and (G,g) is a flat pseudo-Riemannian manifold. For the second case, we see that for any left invariant metric g for which J is an anti-isometry we obtain that the triple (G,g,J) is an anti-Kähler manifold. Besides, given a left invariant anti-Hermitian structure on G we associate a covariant 3-tensor θ on its Lie algebra and prove that such structure is anti-Kähler if and only if θ is a skew-symmetric and pure tensor. From this tensor we classify the real 4-dimensional Lie algebras for which the corresponding Lie group has a left invariant anti-Kähler structure and study the moduli spaces of such structures (up to group isomorphisms that preserve the anti-Kähler structures)
Palabras clave:
ANTI-HERMITIAN GEOMETRY
,
NORDEN METRICS
,
ANTI-KÄHLER MANIFOLD
,
LIE GROUPS
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Identificadores
Colecciones
Articulos(CIEM)
Articulos de CENT.INV.Y ESTUDIOS DE MATEMATICA DE CORDOBA(P)
Articulos de CENT.INV.Y ESTUDIOS DE MATEMATICA DE CORDOBA(P)
Citación
Fernandez Culma, Edison Alberto; Godoy, Yamile Alejandra; Anti-Kählerian geometry on Lie groups; Springer; Mathematical Physics, Analysis And Geometry; 21; 8; 6-3-2018; 1-24
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