Hypercomplex structures associated to quaternionic manifolds

Differential Geometry and its Application

Volumn 9, Issue 3, 1998, Pages 273-292

  Pedersen, H ^a   Poon, Y S ^b   Swann, A F ^c  

^a UNIVERSITY OF SOUTHERN DENMARK   (Denmark)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c University of Bath ^*  (United Kingdom)

Author keywords

Hypercomplex manifold; Instanton; Quaternionic manifold; Self duality; U(2) symmetry

Indexed keywords

EID: 0032324747     PISSN: 09262245     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0926-2245(98)00026-6     Document Type: Article

References (15)

1. [1] D.V. Alekseevsky and S. Marchiafava, Quaternionic structures on a manifold and subordinated structures, Annali di Matematica Pura ed Applicata 171 (1996) 205-273.
2. [2] L. Bérard Bergery and T. Ochiai, On some generalizations of the construction of twistor spaces, in: T.J. Willmore and N. Hitchin, eds., Global Riemannian Geometry (Ellis Horwood, Chichester, 1984) 52-58.
3. [3] A.L. Besse, Einstein Manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, Vol. 10 (Springer, Berlin, 1987).
4. [4] J.F. Glazebrook, F.W. Kamber, H. Pedersen and A. Swann, Foliation reduction and self-duality, in: T. Mitzutani et al., eds., Proceedings of Geometric Study of Foliations, Tokyo, 1993 (World Scientific, Singapore, 1994) 219-249.
5. [5] A. Gray, A note on manifolds whose holonomy group is a subgroup of Sp(n) · Sp(l), Mich. Math. J. 16 (1969) 125-128, 17 (1970) 409.
6. [5] A. Gray, A note on manifolds whose holonomy group is a subgroup of Sp(n) · Sp(l), Mich. Math. J. 16 (1969) 125-128, 17 (1970) 409.
7. [6] D. Joyce, Compact quaternionic and hypercomplex manifolds, J. Differential Geom. 35 (1992) 743-761.
8. [7] S. Marchiafava and G. Romani, Sui fibrati con struttura quaternionale generalizzata, Annali di Matematica Pura ed Applicata 107 (1976) 131-157.
9. [8] M. Obata, Affine connections on manifolds with almost complex, quaternion or Hermitian structure, Jap. J. Math. 26 (1956) 43-79.
10. [9] H. Pedersen and A.F. Swann, Riemannian submersions, four-manifolds and Einstein-Weyl geometry, Proc. London Math. Soc. 66 (1993) 381-399.
11. [10] Y.S. Poon, Compact self-dual manifolds with positive scalar curvature, J. Differential Geom. 24 (1986) 97-132.
12. [11] S.M. Salamon, Differential geometry of quaternionic manifolds, Ann. Scient. Éc. Norm. Sup. 19 (1986) 31-55.
13. [12] N. Steenrod, The Topology of Fibre Bundles. Princeton Mathematical Series 14 (Princeton University Press, 1951).
14. [13] A.F. Swann, HyperKähler and quaternionic Kähler geometry, Math. Ann. 289 (1991) 421-450.
15. [14] J.A. Wolf, Complex homogeneous contact manifolds and quaternionic symmetric spaces, J. Math. Mech. 14 (1965) 1033-1047.