no. 9
Differential geometry
On anti-Hermitian metric connections
[Sur les connexions métriques anti-hermitiennes]

Présenté par : the Editorial Board

Salimov, Arif1
1 Ataturk University, Faculty of Science, Department of Mathematics, 25240, Turkey
Comptes Rendus. Mathématique, Tome 352 (2014) no. 9, pp. 731-735.

C'est un fait remarquable que les métriques anti-kählériennes et leurs métriques jumelles possèdent la même connexion de Levi–Civita. De telles connexions métriques sans torsion mettent aussi en relief l'importance des connexions métriques anti-hermitiennes avec torsion dans l'étude de la géométrie anti-hermitienne. Dans le but de définir de nouveaux types de connexions métriques anti-hermitiennes, nous considérons dans la présente note des classes de variétés anti-hermitiennes associées à ces connexions.

It is a remarkable fact that anti-Kähler and its twin metrics share the same Levi–Civita connection. Such torsion-free metric connection also emphasizes the importance of anti-Hermitian metric connections with torsion in the study of anti-Hermitian geometry. With the objective of defining new types of anti-Hermitian metric connections, in the present paper we consider classes of anti-Hermitian manifolds associated with these connections.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.07.004
Salimov, Arif 1

1 Ataturk University, Faculty of Science, Department of Mathematics, 25240, Turkey 
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Salimov, Arif. On anti-Hermitian metric connections. Comptes Rendus. Mathématique, Tome 352 (2014) no. 9, pp. 731-735. doi : 10.1016/j.crma.2014.07.004. http://www.numdam.org/articles/10.1016/j.crma.2014.07.004/

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☆ The author is grateful to the referee for careful reading and useful comments. This paper is supported by The Scientific and Technological Research Council of Turkey (TUBITAK, Project Number: 112T111).