On Solvable Generalized Calabi-Yau Manifolds

Paolo de Bartolomeis[1]; Adriano Tomassini[2]

  • [1] Università di Firenze Dipartimento di Matematica Applicata G. Sansone Via S. Marta 3 50139 Firenze (Italy)
  • [2] Università di Parma Dipartimento di Matematica Viale G.P. Usberti 53/A 43100 Parma (Italy)

Annales de l’institut Fourier (2006)

  • Volume: 56, Issue: 5, page 1281-1296
  • ISSN: 0373-0956

Abstract

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We give an example of a compact 6-dimensional non-Kähler symplectic manifold ( M , κ ) that satisfies the Hard Lefschetz Condition. Moreover, it is showed that ( M , κ ) is a special generalized Calabi-Yau manifold.

How to cite

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de Bartolomeis, Paolo, and Tomassini, Adriano. "On Solvable Generalized Calabi-Yau Manifolds." Annales de l’institut Fourier 56.5 (2006): 1281-1296. <http://eudml.org/doc/10177>.

@article{deBartolomeis2006,
abstract = {We give an example of a compact 6-dimensional non-Kähler symplectic manifold $(M,\kappa )$ that satisfies the Hard Lefschetz Condition. Moreover, it is showed that $(M,\kappa )$ is a special generalized Calabi-Yau manifold.},
affiliation = {Università di Firenze Dipartimento di Matematica Applicata G. Sansone Via S. Marta 3 50139 Firenze (Italy); Università di Parma Dipartimento di Matematica Viale G.P. Usberti 53/A 43100 Parma (Italy)},
author = {de Bartolomeis, Paolo, Tomassini, Adriano},
journal = {Annales de l’institut Fourier},
keywords = {Symplectic manifolds; Calabi-Yau manifolds; symplectic manifolds; Calabi-Yau-manifolds},
language = {eng},
number = {5},
pages = {1281-1296},
publisher = {Association des Annales de l’institut Fourier},
title = {On Solvable Generalized Calabi-Yau Manifolds},
url = {http://eudml.org/doc/10177},
volume = {56},
year = {2006},
}

TY - JOUR
AU - de Bartolomeis, Paolo
AU - Tomassini, Adriano
TI - On Solvable Generalized Calabi-Yau Manifolds
JO - Annales de l’institut Fourier
PY - 2006
PB - Association des Annales de l’institut Fourier
VL - 56
IS - 5
SP - 1281
EP - 1296
AB - We give an example of a compact 6-dimensional non-Kähler symplectic manifold $(M,\kappa )$ that satisfies the Hard Lefschetz Condition. Moreover, it is showed that $(M,\kappa )$ is a special generalized Calabi-Yau manifold.
LA - eng
KW - Symplectic manifolds; Calabi-Yau manifolds; symplectic manifolds; Calabi-Yau-manifolds
UR - http://eudml.org/doc/10177
ER -

References

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  1. P. de Bartolomeis, Symplectic and Holomorphic Theory in Kähler Geometry, (2004) 
  2. P. de Bartolomeis, A. Tomassini, On the Maslov Index of Lagrangian Submanifolds of Generalized Calabi-Yau Manifolds Zbl1115.53053
  3. P. de Bartolomeis, A. Tomassini, On Formality of Some Symplectic Manifolds, Inter. Math. Res. Notic. 24 (2001), 1287-1314 Zbl1004.53068MR1866746
  4. C. Benson, C. S. Gordon, Kähler and symplectic structures on nilmanifolds, Topology 27 (1988), 513-518 Zbl0672.53036MR976592
  5. A. Blanchard, Sur le variétés analitiques complexes, Ann. Sci. Ecole Norm. Sup. 73 (1956), 157-202 Zbl0073.37503MR87184
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  7. P. Deligne, P. Griffiths, J. Morgan, D. Sullivan, Real Homotopy Theory of Kähler Manifolds, Inventiones Math. 29 (1975), 245-274 Zbl0312.55011MR382702
  8. K. Hasegawa, A note on compact solvmanifolds with Kähler structures, Osaka J. of Math. 43 (2006), 131-135 Zbl1105.32017MR2222405
  9. O. Mathieu, Harmonic cohomology classes of symplectic manifolds, Comm. Math. Helvetici 70 (1995), 1-9 Zbl0831.58004MR1314938
  10. S. A. Merkulov, Formality of Canonical Symplectic Complexes and Frobenius Manifolds, Int. Math. Res. Not. 4 (1998), 727-733 Zbl0931.58002MR1637093
  11. I. Nakamura, Complex parallelisable manifolds and their small deformations, J. of Diff. Geom. 10 (1975), 85-112 Zbl0297.32019MR393580
  12. A. Silva, Spazi omogenei Kähleriani di gruppi di Lie complessi risolubili, Boll. U.M.I. 2 A (1983), 203-210 Zbl0539.32014
  13. D. Yan, Hodge Structure on Symplectic Manifolds, Adv. in Math. 120 (1996), 143-154 Zbl0872.58002MR1392276

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