Article PDF
References
D. V. Alekseevsky,Classification of quaternionic spaces with a transitive solvable group of motions, Math. USSR-Izv.,9 (1975), pp. 297–339.
D. V. Alekseevsky,Conformai mappings of G-structures, Funct. Anal. Appl.,22 (1988), pp. 311–313.
D. V.Alekseevsky - M. M.Graev,G-structures of twistor type, Preprint Dip. Mat. Univ. «La Sapienza», Roma (1991);J. Geom. Phys.,10 (1993) no. 3, pp. 203–229.
D. V. Alekseevsky -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, v. 4 (1993), pp. 43–52, 53–61.
D. V. Alekseevsky -S. Maechiafava,A report on quaternionic-like structures on a manifold, inProceedings of the International Workshop on Differential Geometry and its Applications, Bucarest, July 25–30 1993, Scientific Bulletin UPB, 55, no. 3–4 (1993), pp. 9–34.
D. V. Alekseevsky -S. Marchiafava,Almost quaternionic Hermitian and quasi-Kähler manifolds, inProceedings of the International Workshop on complex structures and vector fields,Sofia,August 20–25 1992, pp. 150–175, Ed. World Scientific, World Scientific, Singapore (1994).
M.Berger,Les groupes d'holonomie homogène des variétés affines et des variétés riemanniennes, Bull. Soc. Math. France (1955), pp. 279–330.
D. Bernard,Sur la géométrie différentielle des G-structures, Ann. Inst. Fourier (Grenoble),10 (1960), pp. 151–270.
A. Besse,Einstein Manifolds, Ergebnisse der Math., 3 Folge, Band 10, Springer-Verlag, Berlin and New York (1987).
D.Blair,Contact Manifolds in Riemannian Geometry, Lectures Notes in Math., n. 509.
E. Bonan,Sur les G-structures de type quaternionien, Cah. Topol. Géom. Diff.,9 (1967), pp. 389–461.
S. S.Chern,On a generalisation of Kähler geometry, inSymposium in Honor of S. Lefschetz on Algebraic Geometry and Topology, Princeton University Press (1957) (Princeton Mathematical Series,18), pp. 103–121.
S. S. Chern,The geometry of G-structures, Bull. Amer. Math. Soc.,72 (1966), pp. 167–219.
S. Fujimura,Q-connections and their changes on almost quaternion manifolds, Hokkaido Math. J.,5 (1976), pp. 239–248.
R. S. Kulkarni,On the principle of uniformisation, J. Diff. Geom.,13 (1978), pp. 109–138.
C. Le Brun -S. Salamon,Strong rigidity of positive quaternionic-Kähler manifolds, Invent. Math.,118 (1994), pp. 109–132.
E. Martinelli,Variétés à structure quaternionienne généralisée, Rev. Roum. Math. Pures Appl., Tome X, n. 7 (1965), pp. 915–922.
E. Musso,On the transformation group of a quaternion manifold, Boll. U.M.I., (7), 6-B (1992), pp. 67–78.
M. Obata,Affine connections on Manifolds with almost complex, quaternion or Hermitian structure, Jap. J. Math.,26 (1956), p. 43.
V. Oproiu,Almost quaternal structures, An. st. Univ. Iazi,23 (1977), pp. 287–298.
V. Oproiu,Integrability of almost quaternal structures, An. st. Univ. «Al. I. Cuza» Iazi,30 (1984), pp. 75–84.
P. Piccinni,On the infinitesimal automorphisms of quaternionic structures, J. Math. Pures Appl.,72 (1993), pp. 593–605.
P. Piccinni -G. Romani,A generalisation of symplectic Pontrjagin classes to vector bundles with structure group Sp(n)·Sp(1), Ann. Mat. Pura Appl. (IV),33 (1983), pp. 1–18.
M. Pontecorvo,Complex structures on quaternionic manifolds, Diff. Geom. Appl.,4 (1994), pp. 163–177.
S. Salamon,Differential geometry of quaternionic manifolds, Ann. Scient. Ec. Norm. Sup., 4ème série,19 (1986), pp. 31–55.
S. Salamon,Riemannian Geometry and Holonomy Groups, Ed. Longman Scientific & Technical, UK (1989).
S.Sternberg,Lectures in Differential Geometry, Prentice-Hall (1964).
A. Swann,HyperKähler and quaternionic Kähler geometry, Math. Ann.,289 (1991), pp. 421–450.
K. Yano -M. Ako,Integrability conditions for almost quaternionic structures, Hokkaido Math. J.,1 (1972), pp. 63–86.
K. Yano -M. Ako,An affine connection in an almost quaternionic manifold, J. Diff. Geom.,8 (1973), pp. 341–347.
Author information
Authors and Affiliations
Additional information
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. (Italy).
Rights and permissions
About this article
Cite this article
Alekseevsky, D.V., Marchiafava, S. Quaternionic structures on a manifold and subordinated structures. Annali di Matematica pura ed applicata 171, 205–273 (1996). https://doi.org/10.1007/BF01759388
Received:
Issue date:
DOI: https://doi.org/10.1007/BF01759388