On non-Kähler compact complex manifolds with balanced and astheno-Kähler metrics

Adela Latorre; Luis Ugarte

doi:10.1016/j.crma.2016.11.004

Differential geometry

On non-Kähler compact complex manifolds with balanced and astheno-Kähler metrics

Presented by: the Editorial Board

Adela Latorre ¹; Luis Ugarte ¹

¹ Departamento de Matemáticas – I.U.M.A., Universidad de Zaragoza, Campus Plaza San Francisco, 50009 Zaragoza, Spain

Comptes Rendus. Mathématique, Volume 355 (2017) no. 1, pp. 90-93.

Abstract
Résumé

In this note, we construct, for every $n \geq 4$ , a non-Kähler compact complex manifold X of complex dimension n admitting a balanced metric and an astheno-Kähler metric, which is in addition k-th Gauduchon for any $1 \leq k \leq n - 1$ .

Dans cette note, nous construisons, pour chaque $n \geq 4$ , une variété compacte complexe non Kähler X de dimension complexe n admettant une métrique equilibrée et une métrique asthéno-Kähler ; de plus, cette métrique est k-ième Gauduchon pour $1 \leq k \leq n - 1$ .

Received: 2016-08-25
Accepted: 2016-11-24
Published online: 2016-12-02

DOI: 10.1016/j.crma.2016.11.004

Author's affiliations:

Adela Latorre ¹; Luis Ugarte ¹

¹ Departamento de Matemáticas – I.U.M.A., Universidad de Zaragoza, Campus Plaza San Francisco, 50009 Zaragoza, Spain

@article{CRMATH_2017__355_1_90_0,
     author = {Adela Latorre and Luis Ugarte},
     title = {On {non-K\"ahler} compact complex manifolds with balanced and {astheno-K\"ahler} metrics},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {90--93},
     publisher = {Elsevier},
     volume = {355},
     number = {1},
     year = {2017},
     doi = {10.1016/j.crma.2016.11.004},
     language = {en},
}

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Adela Latorre; Luis Ugarte. On non-Kähler compact complex manifolds with balanced and astheno-Kähler metrics. Comptes Rendus. Mathématique, Volume 355 (2017) no. 1, pp. 90-93. doi : 10.1016/j.crma.2016.11.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.11.004/

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