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A method of deforming \(G\)-structures. (English) Zbl 1332.53036

The theory of \(G\)-structures has played an important role in the fertile interaction between geometry and physics witnessed among others in the famous work of S. K. Donaldson [J. Differ. Geom. 18, 279–315 (1983; Zbl 0507.57010)] on the classification of 4-manifolds utilizing gauge theory and instantons. The importance of \(G\)-structures in connection with the development of gauge theories and instantons in higher dimensions was quickly realized, and they are still becoming increasingly prominent among physicists due to their natural occurrence in string theory. Among others for these reasons there is a demand for explicit examples of Riemannian manifolds with \(G\)-structures.
In the present paper, the author considers deformations of \(G\)-structures via the right action on the frame bundle of a Riemannian manifold. He investigates which of these deformations again lead to \(G\)-structures and in which cases the original and the deformed \(G\)-structures define the same instantons. Furthermore, he constructs 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 these deformations. The paper finishes with appropriate examples.

MSC:

53C10 \(G\)-structures
81T99 Quantum field theory; related classical field theories

Citations:

Zbl 0507.57010
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References:

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