Abstract
Let (M,Q) be a quaternionic manifold. Conditions for existence of hypercomplex structures H subordinated to the quaternionic structure Q are determined, in particular for a quaternionic Kähler manifold (M,g,Q). Some special systems of almost hypercomplex structures which are admissible for Q are also considered and their relationships with quaternionic transformations are indicated.
Work done under the program of G.N.S.A.G.A. of C.N.R. and partially financed by M.U.R.S.T.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
D.V. Alekseevsky and S. Marchiafava, Quaternionic-like structures on a manifold: Note I. 1-integrability and integrability conditions - Note II, Automorphism groups and their interrelations. Rend. Mat. Acc. Lincei s.9, 4 (1993), 43–52, 53-61
D.V. Alekseevsky and S. Marchiafava, Quaternionic structures on a manifold and subordinated structures. Preprint 94/14 Dipartimento di Matematica “G. Castelnuovo”, Universita’ degli Studi di Roma “La Sapienza”, 1994
D.V. Alekseevsky and S. Marchiafava, Transformation groups of a quaternionic manifold. In preparation
D. Bernard, Sur la géométric differentielle des G-structures. Ann. Inst. Fourier (Grenoble), 10 (1960), 151–270
A. Besse, Einstein manifolds. Ergebnisse der Math. 3 Folge Band 10, Springer-Verlag, Berlin and New York, 1987
E. Bonan, Sur les G-structures de type quaternionien. Cahiers de topologie et géométrie différentielle, 9 (1967), 389–461
S.S. Chern, The geometry of G-structures. Bull. Amer. Math. Soc. 72 (1966), 167–219
S. Fujimura, Q-connections and their changes on almost quaternionic manifolds. Hokkaido Math. J. 5 (1976), 239–248
D. Joyce, Compact hypercomplex and quaternionic manifolds. J. Diff. Geom. 35 (1992), 743–761
D. Joyce Manifolds with many complex structures. Preprint, 1993
R.S. Kulkarni, On the principle of uniformization. J. Diff. Geom., 13 (1978), 109–138
S. Marchiafava, Sulle varietá a struttura quaternionale generalizzata. Rend, di Matematica, 3, ser. VI (1970), 529–545
V. Oproiu, Almost quaternal structures. An. st. Univ. Iazi, 23 (1977), 287–298
V. Oproiu, Integrability of almost quaternal structures. An. st. Univ. “AI.I. Cuza” Iazi 30 (1984), 75–84
P. Piccinni, On the infinitesimal automorphisms of quaternionic structures. J. de Math. Pures et Appl., 72 (1993), 593–605
M. Pontecorvo, Complex structures on quaternionic manifolds. Diff. Geometry and its Applications, 4 (1992), 163–177
S. Salamon, Differential geometry of quaternionic manifolds. Ann. Scient. Ec. Norm. Sup., 4-eme serie 19 (1986), 31–55
S. Salamon, Riemannian geometry and holonomy groups. Ed. Longman Scientific & Technical, UK 1989
A. Swann, HyperKähler and Quaternionic Kahler Geometry. PhD Thesis, Oxford 1990
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Kluwer Academic Publishers
About this chapter
Cite this chapter
Alekseevsky, D.V., Marchiafava, S. (1996). Hypercomplex structures on quaternionic manifolds. In: Tamássy, L., Szenthe, J. (eds) New Developments in Differential Geometry. Mathematics and Its Applications, vol 350. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0149-0_1
Download citation
DOI: https://doi.org/10.1007/978-94-009-0149-0_1
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6553-5
Online ISBN: 978-94-009-0149-0
eBook Packages: Springer Book Archive