Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-27T07:52:04.211Z Has data issue: false hasContentIssue false
  • English
  • Français

Closed Einstein–Weyl structures on compact Sasakian and cosymplectic manifolds

Part of: Global differential geometry

Published online by Cambridge University Press:  11 November 2010

Paola Matzeu
Paola Matzeu
Affiliation:
Dipartimento di Matematica e Informatica, Università degli Studi di Cagliari, Viale Merello 92, 09124 Cagliari, Italy (matzeu@unica.it)
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.

We study closed Einstein–Weyl structures on compact K-contact, Sasakian and cosymplectic manifolds. In particular we prove that compact Sasakian and cosymplectic manifolds endowed with a closed Einstein–Weyl structure are η-Einstein.

Keywords

K-contact manifoldsSasakian manifoldscosymplectic manifoldsEinstein–Weyl structures

MSC classification

Secondary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 54 , Issue 1 , February 2011 , pp. 149 - 160
Copyright
Copyright © Edinburgh Mathematical Society 2010

References

1.Blair, D. E., Riemannian geometry on contact and symplectic manifolds, Progress in Mathematics, Volume 203 (Birkhäuser, 2001).Google Scholar
2.Boyer, C. P. and Galicki, K., On Sasakian-Einstein geometry, Int. J. Math. 11 (2000), 873–909.CrossRefGoogle Scholar
3.Boyer, C. P. and Galicki, K., Einstein manifolds and contact geometry, Proc. Am. Math. Soc. 129 (2001), 2419–2430.CrossRefGoogle Scholar
4.Boyer, C. P. and Galicki, K., Einstein metrics on rational homology spheres, J. Diff. Geom. 74 (2006), 353–362.Google Scholar
5.Boyer, C. P., Galicki, K. and Matzeu, P., On eta-Einstein Sasakian geometry, Commun. Math. Phys. 262 (2006), 177–208.CrossRefGoogle Scholar
6.Boyer, C. P., Galicki, K. and Nakamaye, M., On the geometry of Sasakian–Einstein 5-manifolds, Math. Annalen 325 (2003), 485–524.CrossRefGoogle Scholar
7.Gauduchon, P., Structures de Weyl–Einstein, espaces de twisteurs et variétés de type S 1 × S 3, J. Reine Angew. Math. 469 (1995), 1–50.Google Scholar
8.Ghosh, A., Einstein-Weyl structures on contact metric manifolds, Annals Global Analysis Geom. 35 (2009), 431–441.CrossRefGoogle Scholar
9.Higa, T., Weyl manifolds and Einstein-Weyl manifolds, Commun. Math. Univ. Saint Pauli 42 (1993), 143–160.Google Scholar
10.Matzeu, P., Some examples of Einstein-Weyl structures on almost contact manifolds, Class. Quant. Grav. 17 (2000), 1–9.CrossRefGoogle Scholar
11.Matzeu, P., Almost contact Einstein-Weyl structures, Manuscr. Math. 108 (2002), 275–288.CrossRefGoogle Scholar
12.Narita, F., Riemannian submersions and Riemannian manifolds with Einstein-Weyl structures, Geom. Dedicata 65 (1997), 103–116.CrossRefGoogle Scholar
13.Narita, F., Einstein-Weyl structures on almost contact metric manifolds, Tsukuba J. Math. 22 (1998), 87–98.CrossRefGoogle Scholar
14.Okumura, M., Some remarks on space with a certain contact structure, Tohoku Math. J. 14 (1962), 135–145.CrossRefGoogle Scholar
15.Ornea, L. and Piccinni, P., Compact hyperhermitian Weyl and quaternionic Hermitian Weyl manifolds, Annals Global Analysis Geom. 16(4) (1998), 383–398.CrossRefGoogle Scholar
16.Pedersen, H., Poon, Y. S. and Swann, A., The Einstein-Weyl equations in complex and quaternionic geometry, Diff. Geom. Applic. 3 (1993), 309–321.CrossRefGoogle Scholar
17.Tachibana, S., On harmonic tensors in compact Sasakian spaces, Tohoku Math. J. 17 (1965), 271–284.CrossRefGoogle Scholar
18.Tondeur, P., Geometry of foliations, Monographs in Mathematics, Volume 90 (Birkhäuser, 1997).Google Scholar