Generalized Kaehler manifolds with split tangent bundle

TL;DR

This paper classifies certain compact four-dimensional generalized Kaehler manifolds with commuting complex structures that induce opposite orientations, expanding understanding of their geometric structure.

Contribution

It provides a complete classification of compact generalized Kaehler four-manifolds with commuting complex structures and opposite orientations.

Findings

Complete classification of these manifolds.

Identification of conditions for commuting complex structures.

Insights into the orientation properties of the structures.

Abstract

We study generalized Kaehler manifolds for which the corresponding complex structures commute and classify completely the compact generalized Kaehler four-manifolds for which the induced complex structures yield opposite orientations.