Weekly seminar on March 11, 2015, 10.00 will feature a report by Arif Salimov, Professor Department of Mathematics Faculty of Science, Ataturk University, Turkey, entitled “Recent Developments in Anti-Hermitian Geometry”.
We introduced the notion of an anti-Kahler Codazzi manifold, for which a twin anti-Hermitian (also known as a twin Norden) metric of neutral signature satisfies the Codazzi equation. We introduced also the notion Ricci* tensor field for Levi-Civita connection of an anti-Hermitian metric and give a characterization of an anti-Kahler-Codazzi manifold in terms of a Ricci* tensor field . Such torsion-free metric connection also emphasise the importance of anti-Hermitian metric connections with torsion in the study of anti-Kahler-Codazzi geometry. With the objective of defining new types of anti-Hermitian metric connections, we consider properties of anti-Hermitian manifolds associated to these connections.