Comptes Rendus
no. 1
Differential Geometry
Homogeneous quaternionic Kähler structures of linear type
[Structures quaternion-kählériennes homogènes de type linéaire]

Présenté par : Marcel Berger

Marco Castrillón López1 ; Pedro M. Gadea2 ; Andrew Swann3
1 Department of Geometry and Topology, Faculty of Mathematics, Avda. Complutense s/n, 28040 Madrid, Spain
2 Institute of Mathematics and Fundamental Physics, CSIC, Serrano 144, 28006, Madrid, Spain
3 Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, DK 5230 Odense M, Denmark
Comptes Rendus. Mathématique, Volume 338 (2004) no. 1, pp. 65-70.

Nous donnons une classification des structures kählériennes quaternioniennes homogènes en termes de tenseurs réels, ainsi qu'une rélation avec la décomposition donnée par Fino en utilisant la théorie des représentations. Nous donnons aussi une rélation entre les modules ayant dimension à croissance linéaire et l'espace hyperbolique quaternionien.

A classification of homogeneous quaternionic Kähler structures by real tensors is given and related to Fino's representation theoretic decomposition. A relationship between the modules whose dimension grows linearly and quaternionic hyperbolic space is found.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2003.10.035
Marco Castrillón López 1 ; Pedro M. Gadea 2 ; Andrew Swann 3

1 Department of Geometry and Topology, Faculty of Mathematics, Avda. Complutense s/n, 28040 Madrid, Spain
2 Institute of Mathematics and Fundamental Physics, CSIC, Serrano 144, 28006, Madrid, Spain
3 Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, DK 5230 Odense M, Denmark 
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     title = {Homogeneous quaternionic {K\"ahler} structures of linear type},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {65--70},
     publisher = {Elsevier},
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     language = {en},
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Marco Castrillón López; Pedro M. Gadea; Andrew Swann. Homogeneous quaternionic Kähler structures of linear type. Comptes Rendus. Mathématique, Volume 338 (2004) no. 1, pp. 65-70. doi : 10.1016/j.crma.2003.10.035. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2003.10.035/

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