Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-25T08:13:44.444Z Has data issue: false hasContentIssue false
  • English
  • Français

THREE-FORMS AND ALMOST COMPLEX STRUCTURES ON SIX-DIMENSIONAL MANIFOLDS

Part of: General theory of differentiable manifolds Global differential geometry

Published online by Cambridge University Press:  01 April 2008

MARTIN PANÁK  and
JIŘÍ VANŽURA
MARTIN PANÁK*
Affiliation:
Department of Algebra and Geometry, Masaryk University Brno, Janackovo nam. 2a, 602 00 Brno, Czech Republic (email: [email protected])
JIŘÍ VANŽURA
Affiliation:
Institute of Mathematics, AS CR, Zizkova 22, 616 62 Brno, Czech Republic (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper deals with 3-forms on six-dimensional manifolds, the first dimension where the classification of 3-forms is not trivial. It includes three classes of multisymplectic 3-forms. We study the class which is closely related to almost complex structures.

Keywords

3-formalmost complex structuresix-dimensional manifold

MSC classification

Secondary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.) 58A10: Differential forms
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 84 , Issue 2 , April 2008 , pp. 247 - 263
Copyright
Copyright © 2008 Australian Mathematical Society

References

[1]Friedrich, T., ‘Spin(9)-structures and connections with totally skew-symmetric torsion’, J. Geom. Phys. 47(2) (2003), 197–206.CrossRefGoogle Scholar
[2]Hitchin, N., ‘The geometry of three-forms in six dimensions’, J. Differential Geom. 55 (2000), 547–576.CrossRefGoogle Scholar
[3]Joyce, D. D., Compact Manifolds with Special Holonomy, Oxford Mathematical Monographs (Oxford University Press, Oxford, 2000).CrossRefGoogle Scholar
[4]Vanžura, J., ‘One kind of multisymplectic structures on 6-manifolds steps in differential geometry’, Proceedings of the Colloquium on Differential Geometry, Debrecen, Hungary, 25–30 July, 2000, pp. 375–391.Google Scholar
[5]Witt, F., ‘Special metric structures and closed forms’, PhD thesis, 2005, Oxford, arxiv:math.DG/0502443.Google Scholar