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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On deformations of compact balanced manifolds


Authors: Alberto Saracco and Adriano Tomassini
Journal: Proc. Amer. Math. Soc. 139 (2011), 641-653
MSC (2010): Primary 53C15; Secondary 32G05
Published electronically: September 23, 2010
MathSciNet review: 2736345
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Abstract: We study suitable deformations of the complex structure on a compact balanced manifold $ (M,J,g,\omega)$, naturally associated with cohomology classes in $ H^2(M,\mathbb{R})$. We construct curves of balanced structures on a compact holomorphically parallelizable $ 5$-dimensional complex nilmanifold and of half-flat structures on a compact complex $ 3$-dimensional solvmanifold respectively.


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Additional Information

Alberto Saracco
Affiliation: Dipartimento di Matematica, Università di Parma, Parco Area delle Scienze 53/A, I-43124 Parma, Italy
Email: alberto.saracco@unipr.it

Adriano Tomassini
Affiliation: Dipartimento di Matematica, Università di Parma, Parco Area delle Scienze 53/A, I-43124 Parma, Italy
Email: adriano.tomassini@unipr.it

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10559-2
PII: S 0002-9939(2010)10559-2
Keywords: Balanced metric, half-flat structure, deformation
Received by editor(s): March 3, 2010
Published electronically: September 23, 2010
Additional Notes: This work was supported by the Project M.I.U.R. “Geometric Properties of Real and Complex Manifolds” and by G.N.S.A.G.A. of I.N.d.A.M
Communicated by: Franc Forstneric
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.