Some remarks on quaternion-Hermitian manifolds

Andrew Swann

Archivum Mathematicum (1997)

  • Volume: 033, Issue: 4, page 349-354
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Swann, Andrew. "Some remarks on quaternion-Hermitian manifolds." Archivum Mathematicum 033.4 (1997): 349-354. <http://eudml.org/doc/248026>.

@article{Swann1997,
abstract = {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.},
author = {Swann, Andrew},
journal = {Archivum Mathematicum},
keywords = {G-structure; quaternion-Hermitian manifold; nearly-quaternionic Kähler; semi-quaternionic Kähler; fundamental four-form; -structure; quaternionic Hermitian manifold; quaternionic Kähler manifold; nearly-quaternionic Kähler manifold; semi-quaternionic Kähler manifold},
language = {eng},
number = {4},
pages = {349-354},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Some remarks on quaternion-Hermitian manifolds},
url = {http://eudml.org/doc/248026},
volume = {033},
year = {1997},
}

TY - JOUR
AU - Swann, Andrew
TI - Some remarks on quaternion-Hermitian manifolds
JO - Archivum Mathematicum
PY - 1997
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 033
IS - 4
SP - 349
EP - 354
AB - 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.
LA - eng
KW - G-structure; quaternion-Hermitian manifold; nearly-quaternionic Kähler; semi-quaternionic Kähler; fundamental four-form; -structure; quaternionic Hermitian manifold; quaternionic Kähler manifold; nearly-quaternionic Kähler manifold; semi-quaternionic Kähler manifold
UR - http://eudml.org/doc/248026
ER -

References

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  1. Sur l’algèbre extérieure d’une variété presque hermitienne quaternionique, C. R. Acad. Sci. Paris 295 (1982), 115–118. (1982) MR0676377
  2. Representations of Compact Lie Groups, Graduate Texts in Math., 98, Springer, 1985. (1985) MR0781344
  3. Variedades cuaternionicas y G 2 -variadades, Ph. D. Thesis, Univ. de La Laguna. 
  4. Quaternion Kählerian manifolds, J. Differ. Geom. 9 (1974), 483–500. (1974) Zbl0297.53014MR0348687
  5. Variedades cuaterniónicas no-kählerianas, Publ. Depto. Geom. y Top., Univ. de Santiago 62 (1984). (1984) 
  6. Quaternionic Kähler manifolds, Invent. Math. 67 (1982), 143–171. (1982) Zbl0486.53048MR0664330
  7. Aspects symplectiques de la géométrie quaternionique, C. R. Acad. Sci. Paris 308 (1989), 225–228. (1989) Zbl0661.53023MR0986384
  8. 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. (1989) MR1089891
  9. HyperKähler and quaternionic Kähler geometry, Math. Ann. 289 (1991). (1991) Zbl0711.53051MR1096180

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