Conformal Killing 2-forms on four-dimensional manifolds

We study four-dimensional simply connected Lie groups G with a left invariant Riemannian metric g admitting non-trivial conformal Killing 2-forms. We show that either the real line defined by such a form is invariant under the group action, or the metric is half-conformally flat. In the first case,...

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Detalles Bibliográficos
Autores: Andrada, Adrián Marcelo, Barberis, Maria Laura Rita, Moroianu, Andrei
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2016
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/59789
Acceso en línea:http://hdl.handle.net/11336/59789
Access Level:acceso abierto
Palabra clave:CONFORMAL KILLING FORMS
HALF-CONFORMALLY FLAT METRICS
INVARIANT CONFORMALLY KÄHLER STRUCTURES
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario:We study four-dimensional simply connected Lie groups G with a left invariant Riemannian metric g admitting non-trivial conformal Killing 2-forms. We show that either the real line defined by such a form is invariant under the group action, or the metric is half-conformally flat. In the first case, the problem reduces to the study of invariant conformally Kähler structures, whereas in the second case, the Lie algebra of G belongs (up to homothety) to a finite list of families of metric Lie algebras.