no. 21-22
Differential geometry
On an isotropic property of anti-Kähler–Codazzi manifolds
[Sur une propriété isotrope des variétés anti-Kähler–Codazzi]

Présenté par : the Editorial Board

Salimov, Arif1 ; Akbulut, Kursat1 ; Turanli, Sibel2
1 Ataturk University, Faculty of Science, Dep. of Mathematics, 25240, Turkey
2 Erzurum Technical University, Faculty of Science, Dep. of Mathematics, Erzurum, Turkey
Comptes Rendus. Mathématique, Tome 351 (2013) no. 21-22, pp. 837-839.

Nous donnons une preuve du fait quʼune variété de type anti-Kähler–Codazzi se réduit à une variété isotrope du même type si et seulement si le champ de tenseurs de Ricci coïncide avec le champ de tenseurs de Ricci*.

We give a proof of the fact that an anti-Kähler–Codazzi manifold reduces to an isotropic anti-Kähler manifold if and only if the Ricci tensor field coincides with the Ricci* tensor field.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.09.020
Salimov, Arif 1 ; Akbulut, Kursat 1 ; Turanli, Sibel 2

1 Ataturk University, Faculty of Science, Dep. of Mathematics, 25240, Turkey
2 Erzurum Technical University, Faculty of Science, Dep. of Mathematics, Erzurum, Turkey 
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Salimov, Arif; Akbulut, Kursat; Turanli, Sibel. On an isotropic property of anti-Kähler–Codazzi manifolds. Comptes Rendus. Mathématique, Tome 351 (2013) no. 21-22, pp. 837-839. doi : 10.1016/j.crma.2013.09.020. http://www.numdam.org/articles/10.1016/j.crma.2013.09.020/

[1] García-Río, E.; Matsushita, Y. Isotropic Kähler structures on Engel 4-manifolds, J. Geom. Phys., Volume 33 (2000), pp. 288-294

[2] Salimov, A. Tensor Operators and Their Applications, Nova Science Publishers, New York, 2012

[3] Salimov, A.; Turanli, S. Curvature properties of anti-Kähler–Codazzi manifolds, C. R. Acad. Sci. Paris, Ser. I, Volume 351 (2013) no. 5–6, pp. 225-227

[4] Tachibana, S. Analytic tensor and its generalization, Tohoku Math. J., Volume 12 (1960) no. 2, pp. 208-221

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