Homogeneous quaternionic Kähler structures of linear type

Marco Castrillón López; Pedro M. Gadea; Andrew Swann

doi:10.1016/j.crma.2003.10.035

Differential Geometry

Homogeneous quaternionic Kähler structures of linear type

Presented by: Marcel Berger

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

Comptes Rendus. Mathématique, Volume 338 (2004) no. 1, pp. 65-70.

Abstract
Résumé

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.

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.

Received: 2003-08-10
Accepted: 2003-10-31
Published online: 2003-12-11

DOI: 10.1016/j.crma.2003.10.035

Author's affiliations:

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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     author = {Marco Castrill\'on~L\'opez and Pedro M. Gadea and Andrew Swann},
     title = {Homogeneous quaternionic {K\"ahler} structures of linear type},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {65--70},
     publisher = {Elsevier},
     volume = {338},
     number = {1},
     year = {2004},
     doi = {10.1016/j.crma.2003.10.035},
     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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