Other Classes of Tangent Bundles with General Natural Almost Anti-Hermitian Structures

TL;DR

This paper investigates specific anti-Hermitian structures on tangent bundles, providing conditions for their classification into known classes and characterizing anti-Kahlerian structures with precise criteria.

Contribution

It offers a comprehensive analysis of general natural anti-Hermitian structures on tangent bundles, including classification conditions and characterization of anti-Kahlerian structures.

Findings

Conditions for structures to belong to eight classes by Ganchev and Borisov

Necessary and sufficient conditions for anti-Kahlerian structures

Results on remaining classes of structures

Abstract

We continue the study of 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. 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.