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On the existence of balanced and SKT metrics on nilmanifolds


Authors: Anna Fino and Luigi Vezzoni
Journal: Proc. Amer. Math. Soc. 144 (2016), 2455-2459
MSC (2010): Primary 32J27; Secondary 53C55, 53C30, 53D05
DOI: https://doi.org/10.1090/proc/12954
Published electronically: January 27, 2016
MathSciNet review: 3477061
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Abstract: On a complex manifold a Hermitian metric which is simultaneously SKT and balanced has to be necessarily Kähler. It has been conjectured that if a compact complex manifold $ (M, J)$ has an SKT metric and a balanced metric both compatible with $ J$, then $ (M, J)$ is necessarily Kähler. We show that the conjecture is true for nilmanifolds.


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Additional Information

Anna Fino
Affiliation: Dipartimento di Matematica G. Peano, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy
Email: annamaria.fino@unito.it

Luigi Vezzoni
Affiliation: Dipartimento di Matematica G. Peano, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy
Email: luigi.vezzoni@unito.it

DOI: https://doi.org/10.1090/proc/12954
Keywords: Special Hermitian metrics, nilmanifolds
Received by editor(s): July 2, 2105
Published electronically: January 27, 2016
Additional Notes: This work was partially supported by the project PRIN, Varietà reali e complesse: geometria, topologia e analisi armonica, the project FIRB, Differential Geometry and Geometric functions theory and by GNSAGA (Indam) of Italy
Communicated by: Lei Ni
Article copyright: © Copyright 2016 American Mathematical Society