On anti-Hermitian metric connections

It is a remarkable fact that anti-Kahler 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. (C) 2014 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.