Utilize este identificador para referenciar este registo:
https://hdl.handle.net/1822/34707
Título: | The classification of naturally reductive homogeneous spaces in dimensions n≤6 |
Autor(es): | Ferreira, Ana Cristina Agricola, Ilka Friedrich, Thomas |
Palavras-chave: | naturally reductive homogeneous space connection with skew torsion characteristic connection holonomy algebra quasi-Sasakian manifold almost complex manifold |
Data: | Abr-2015 |
Editora: | Elsevier |
Revista: | Differential Geometry and its Applications |
Resumo(s): | We 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. |
Tipo: | Artigo |
URI: | https://hdl.handle.net/1822/34707 |
DOI: | 10.1016/j.difgeo.2014.11.005 |
ISSN: | 0926-2245 |
Versão da editora: | http://www.sciencedirect.com/science/article/pii/S092622451400165X |
Arbitragem científica: | yes |
Acesso: | Acesso restrito UMinho |
Aparece nas coleções: | CMAT - Artigos em revistas com arbitragem / Papers in peer review journals |
Ficheiros deste registo:
Ficheiro | Descrição | Tamanho | Formato | |
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nat-red.pdf Acesso restrito! | Documento principal | 426,5 kB | Adobe PDF | Ver/Abrir |