[Une Note sur les petites déformations des variétés équilibrées]
Dans cette Note nous montrons que, sous une condition plus faible que le lemme du , lʼexistence de métriques équilibrées est préservée par des petites déformations. Cette condition affaiblie est satisfaite par lʼespace des twisteurs sur une variété différentielle de dimension 4, compacte et auto-duale.
In this Note we prove that, under a weaker condition than the -lemma, the existence of balanced metrics is preserved under small deformations. This weaker condition is satisfied on the twistor space over a compact self-dual four manifold.
Accepté le :
Publié le :
@article{CRMATH_2011__349_13-14_793_0,
author = {Fu, Jixiang and Yau, Shing-Tung},
title = {A {Note} on small deformations of balanced manifolds},
journal = {Comptes Rendus. Math\'ematique},
pages = {793--796},
publisher = {Elsevier},
volume = {349},
number = {13-14},
year = {2011},
doi = {10.1016/j.crma.2011.06.023},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2011.06.023/}
}
TY - JOUR AU - Fu, Jixiang AU - Yau, Shing-Tung TI - A Note on small deformations of balanced manifolds JO - Comptes Rendus. Mathématique PY - 2011 SP - 793 EP - 796 VL - 349 IS - 13-14 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2011.06.023/ DO - 10.1016/j.crma.2011.06.023 LA - en ID - CRMATH_2011__349_13-14_793_0 ER -
%0 Journal Article %A Fu, Jixiang %A Yau, Shing-Tung %T A Note on small deformations of balanced manifolds %J Comptes Rendus. Mathématique %D 2011 %P 793-796 %V 349 %N 13-14 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2011.06.023/ %R 10.1016/j.crma.2011.06.023 %G en %F CRMATH_2011__349_13-14_793_0
Fu, Jixiang; Yau, Shing-Tung. A Note on small deformations of balanced manifolds. Comptes Rendus. Mathématique, Tome 349 (2011) no. 13-14, pp. 793-796. doi : 10.1016/j.crma.2011.06.023. http://www.numdam.org/articles/10.1016/j.crma.2011.06.023/
[1] Small deformations of a class of compact non-Kähler manifolds, Proc. Amer. Math. Soc., Volume 109 (1990), pp. 1059-1062
[2] Metric properties of manifolds bimeromorphic to compact Kähler spaces, J. Diff. Geom., Volume 37 (1993), pp. 95-121
[3] Modifications of compact balanced manifolds, C. R. Acad. Sci. Paris, Sér. I, Volume 320 (1995), pp. 1517-1522
[4] Real homotopy theory of Kähler manifolds, Invent. Math., Volume 29 (1975), pp. 245-274
[5] The Frölicher spectral sequence on a twistor space, J. Diff. Geom., Volume 38 (1993), pp. 653-669
[6] Balanced metrics on non-Kähler Calabi–Yau threefolds (A new version of) | arXiv
[7] Structures de Weyl et théorèmes dʼannulation sur une variété conforme autoduale, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), Volume 18 (1991), pp. 563-629
[8] On deformations of complex analytic structures. III. Stability theorems for complex structures, Ann. of Math. (2), Volume 71 (1960), pp. 43-76
[9] On the existence of special metrics in complex geometry, Acta Math., Volume 149 (1982), pp. 261-295
[10] Complex Manifolds, Holt, Rinehart and Winston, Inc., 1971
[11] Deformations openness and closedness of various classes of compact complex manifolds; examples | arXiv
[12] C.-C. Wu, On the geometry of superstrings with torsion, thesis, Department of Mathematics, Harvard University, Cambridge, MA 02138, USA, April 2006.
[13] Twistor spaces and balanced metrics on complex manifolds http://www.math.ucla.edu/~greene/YauTwister(8-9).pdf (One topic of a series of lectures at Department of Mathematics, UCLA in Spring 2007. The notes were taken by R. Greene)
Cité par Sources :
