On the local structure of generalized Kaehler manifolds

TL;DR

This paper investigates the local geometric structure of generalized Kaehler manifolds, focusing on conditions that ensure the closedness of the 2-form b within the bihermitian framework.

Contribution

It establishes natural integrability conditions that guarantee the 2-form b is closed in the context of generalized Kaehler geometry.

Findings

Identifies conditions for db=0 in bihermitian structures

Provides insights into the local structure of generalized Kaehler manifolds

Enhances understanding of integrability in generalized complex geometry

Abstract

Let (g,b,J_+,J_-) be the bihermitian structure corresponding to a generalized Kaehler structure. We find natural integrability conditions under which db=0.