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Keywords:
G-structure; quaternion-Hermitian manifold; nearly-quaternionic Kähler; semi-quaternionic Kähler; fundamental four-form
Summary:
Nearly-quaternionic Kähler manifolds of dimension at least $8$ are shown to be quaternionic Kähler. Restrictions on the covariant derivative of the fundamental four-form of a semi-quaternionic Kähler are also found.
References:
[B] Bonan, E.: Sur l’algèbre extérieure d’une variété presque hermitienne quaternionique. C. R. Acad. Sci. Paris 295 (1982), 115–118. MR 0676377
[BtD] Bröcker, T., tom Dieck, T.: Representations of Compact Lie Groups. Graduate Texts in Math., 98, Springer, 1985. MR 0781344
[C] Cabrera, F. M.: Variedades cuaternionicas y $G_2$-variadades. Ph. D. Thesis, Univ. de La Laguna.
[I] Ishihara, S.: Quaternion Kählerian manifolds. J. Differ. Geom. 9 (1974), 483–500. MR 0348687 | Zbl 0297.53014
[M] Moreiras, B. R.: Variedades cuaterniónicas no-kählerianas. Publ. Depto. Geom. y Top., Univ. de Santiago 62 (1984).
[Sa] Salamon, S. M.: Quaternionic Kähler manifolds. Invent. Math. 67 (1982), 143–171. MR 0664330 | Zbl 0486.53048
[Sw1] Swann, A. F.: Aspects symplectiques de la géométrie quaternionique. C. R. Acad. Sci. Paris 308 (1989), 225–228. MR 0986384 | Zbl 0661.53023
[Sw2] Swann, A. F.: Quaternionic Kähler geometry and the fundamental $4$-from. Proceedings of the Curvature Geometry Workshop, Lancaster, C. T. J. Dodson (ed.), UDLM Publ., 1989, pp. 165–174. MR 1089891
[Sw3] Swann, A. F.: HyperKähler and quaternionic Kähler geometry. Math. Ann. 289 (1991). MR 1096180 | Zbl 0711.53051
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