Comptes Rendus
no. 21-22
Differential geometry
On an isotropic property of anti-Kähler–Codazzi manifolds
Presented by: the Editorial Board
Arif Salimov 1 ; Kursat Akbulut 1 ; Sibel Turanli 2
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, Volume 351 (2013) no. 21-22, pp. 837-839

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.

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*.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2013.09.020

Arif Salimov  1 ; Kursat Akbulut  1 ; Sibel Turanli  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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     title = {On an isotropic property of {anti-K\"ahler{\textendash}Codazzi} manifolds},
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Arif Salimov; Kursat Akbulut; Sibel Turanli. On an isotropic property of anti-Kähler–Codazzi manifolds. Comptes Rendus. Mathématique, Volume 351 (2013) no. 21-22, pp. 837-839. doi: 10.1016/j.crma.2013.09.020

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

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

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

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