Other classes of tangent bundles with general natural almost anti-Hermitian structures

We continue the study initiated by Oproiu in [21], concerning the anti-Hermitian structures of general natural lift type on the tangent bundles. We get the conditions under which these structures are in the eight classes obtained by Ganchev and Borisov in [8]. We complete the characterization of the general natural anti-Kahlerian structures on the tangent bundles with necessary and sufficient conditions, then we present some results concerning the remaining classes.