We introduce a property of compact complex manifolds under which the existence of balanced metric is stable by small deformations of the complex structure. This property, which is weaker than the ∂∂⎯⎯⎯-Lemma, is characterized in terms of the strongly Gauduchon cone and of the first ∂∂⎯⎯⎯-degree measuring the difference of Aeppli and Bott-Chern cohomologies with respect to the Betti number b1.
On small deformations of balanced manifolds / Angella, Daniele; Luis, Ugarte. - In: DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS. - ISSN 0926-2245. - ELETTRONICO. - 54:(2017), pp. 464-474. [10.1016/j.difgeo.2017.07.010]
On small deformations of balanced manifolds
ANGELLA, DANIELE;
2017
Abstract
We introduce a property of compact complex manifolds under which the existence of balanced metric is stable by small deformations of the complex structure. This property, which is weaker than the ∂∂⎯⎯⎯-Lemma, is characterized in terms of the strongly Gauduchon cone and of the first ∂∂⎯⎯⎯-degree measuring the difference of Aeppli and Bott-Chern cohomologies with respect to the Betti number b1.
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