Goto's generalized Kaehler stability theorem

TL;DR

This paper provides a concise and direct proof of Goto's generalized Kaehler stability theorem, showing that small deformations of the structure can be maintained while preserving its properties.

Contribution

It offers a simplified proof of the stability theorem for generalized Kaehler structures, enhancing understanding and potential applications.

Findings

Proof of stability under small deformations

Conditions for J_2 determined by a closed form

Maintenance of generalized Kaehler structure during deformation

Abstract

In these notes we give a shortened and more direct proof of Goto's generalized Kaehler stability theorem stating that if (J_1,J_2) is a generalized kaehler structure for which J_2 is determined by a nowhere vanishing closed form, then small deformations of J_1 can be coupled with small deformations of J_2 so that the pair remains a generalized Kaehler structure.