A method of deforming G-structures

TL;DR

This paper studies how G-structures can be deformed through frame bundle actions, analyzing when these deformations preserve the structure and instanton properties, and exploring the effects on compatible connections and intrinsic torsion.

Contribution

It introduces a new method for deforming G-structures via frame bundle actions and examines the resulting geometric and connection-related properties.

Findings

Identifies conditions under which deformations preserve G-structures.

Establishes a bijection between compatible connections before and after deformation.

Analyzes how intrinsic torsion changes under these deformations.

Abstract

We consider deformations of G-structures via the right action on the frame bundle in a base-point-dependent manner. We investigate which of these deformations again lead to G-structures and in which cases the original and the deformed G-structures define the same instantons. Further, we construct a bijection from connections compatible with the original G-structure to those compatible with the deformed G-structure and investigate the change of intrinsic torsion under the aforementioned deformations. Finally, we consider several examples.