Utilize este identificador para referenciar este registo: http://hdl.handle.net/1822/34707

TítuloThe classification of naturally reductive homogeneous spaces in dimensions n≤6
AutorFerreira, Ana Cristina
Agricola, Ilka
Friedrich, Thomas
Palavras-chavenaturally reductive homogeneous space
connection with skew torsion
characteristic connection
holonomy algebra
quasi-Sasakian manifold
almost complex manifold
ResumoWe present a new method for classifying naturally reductive homogeneous spaces – i.e.homogeneous Riemannian manifolds admitting a metric connection with skew torsion that has parallel torsion and curvature. This method is based on a deeper understanding of the holonomy algebra of connections with parallel skew torsion on Riemannian manifolds and the interplay of such a connection with the geometric structure on the given Riemannian manifold. It allows to reproduce by easier arguments the known classifications in dimensions 3, 4, and 5, and yields as a new result the classification in dimension 6. In each dimension, one obtains a ‘hierarchy’ of degeneracy for the torsion form, which we then treat case by case. For the completely degenerate cases, we obtain results that are independent of the dimension. In some situations, we are able to prove that any Riemannian manifold with parallel skew torsion has to be naturally reductive. We show that a ‘generic’ parallel torsion form defines a quasi-Sasakian structure in dimension 5 and an almost complex structure in dimension 6.
Versão da editorahttp://www.sciencedirect.com/science/article/pii/S092622451400165X
Arbitragem científicayes
Aparece nas coleções:CMAT - Artigos com arbitragem/Papers with refereeing

Ficheiros deste registo:
Ficheiro Descrição TamanhoFormato 
nat-red.pdfDocumento principal426,5 kBAdobe PDFVer/Abrir  Solicitar cópia ao autor!

Partilhe no FacebookPartilhe no TwitterPartilhe no DeliciousPartilhe no LinkedInPartilhe no DiggAdicionar ao Google BookmarksPartilhe no MySpacePartilhe no Orkut
Exporte no formato BibTex mendeley Exporte no formato Endnote Adicione ao seu Currículo DeGóis