Comptes Rendus
no. 1
Classification of positive quaternion-Kähler 12-manifolds
[Classification de variétés Kähleriennes quaternioniques positives de dimension 12]
Haydeé Herrera1 ; Rafael Herrera2
1 Department of Mathematics, Tufts University, Medford, MA 02155, USA
2 Department of Mathematics, University of California, Riverside, CA 92521, USA
Comptes Rendus. Mathématique, Volume 334 (2002) no. 1, pp. 43-46.

Dans cette Note, nous démontrons que les variétés complètes Kähleriennes quaternioniques de courbure scalaire positive et de dimension 12 appartiennent à la liste d'espaces symétriques donnée par Wolf [12].

We prove that the 12-dimensional complete quaternion-Kähler manifolds with positive scalar curvature belong to the list of symmetric spaces given by Wolf [12].

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02209-4
Haydeé Herrera 1 ; Rafael Herrera 2

1 Department of Mathematics, Tufts University, Medford, MA 02155, USA
2 Department of Mathematics, University of California, Riverside, CA 92521, USA 
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Haydeé Herrera; Rafael Herrera. Classification of positive quaternion-Kähler $ \mathrm{12}$-manifolds. Comptes Rendus. Mathématique, Volume 334 (2002) no. 1, pp. 43-46. doi : 10.1016/S1631-073X(02)02209-4. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02209-4/

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[3] Herrera R., Ph.D. thesis, Oxford, 1997

[4] Herrera H., Herrera R., A ^-genus on non-spin manifolds with S1 actions and the classification of positive quaternion-Kähler 12-manifolds, IHÉS Preprint, 2001

[5] Herrera H., Herrera R., Elliptic genus on non-spin manifolds, Preprint, 2001

[6] N. Hitchin Kählerian twistor spaces, Proc. London Math. Soc., Volume 43 (1981) no. 3, pp. 133-150

[7] C. LeBrun Fano manifolds, contact structures, and quaternionic geometry, Internat. J. Math., Volume 6 (1995) no. 3, pp. 419-437

[8] C.R. LeBrun; S.M. Salamon Strong rigidity of positive quaternion-Kähler manifolds, Invent. Math., Volume 118 (1994), pp. 109-132

[9] F. Podestà; L. Verdiani A note on quaternion-Kähler manifolds, Internat. J. Math., Volume 11 (2000) no. 2, pp. 279-283

[10] Y.S. Poon; S.M. Salamon Eight-dimensional quaternionic Kähler manifolds with positive scalar curvature, J. Differential Geometry, Volume 33 (1991), pp. 363-378

[11] S.M. Salamon Quaternionic Kähler manifolds, Invent. Math., Volume 67 (1982), pp. 143-171

[12] J.A. Wolf Complex homogeneous contact structures and quaternionic symmetric spaces, J. Math. Mech., Volume 14 (1965), pp. 1033-1047

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