Deformations of $$\mathrm {G}_2$$-instantons on nearly $$\mathrm {G}_2$$ manifolds

We study the deformation theory of $$\mathrm {G}_2$$ G 2 -instantons on nearly $$\mathrm {G}_2$$ G 2 manifolds. There is a one-to-one correspondence between nearly parallel $$\mathrm {G}_2$$ G 2 structures and real Killing spinors; thus, the deformation theory can be formulated in terms of spinors a...

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Bibliographic Details
Published in:Annals of global analysis and geometry 2022-09, Vol.62 (2), p.329-366
Main Author: Singhal, Ragini
Format: Article
Language:English
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Summary:We study the deformation theory of $$\mathrm {G}_2$$ G 2 -instantons on nearly $$\mathrm {G}_2$$ G 2 manifolds. There is a one-to-one correspondence between nearly parallel $$\mathrm {G}_2$$ G 2 structures and real Killing spinors; thus, the deformation theory can be formulated in terms of spinors and Dirac operators. We prove that the space of infinitesimal deformations of an instanton is isomorphic to the kernel of an elliptic operator. Using this formulation we prove that abelian instantons are rigid. Then we apply our results to describe the deformation space of the characteristic connection on the four normal homogeneous nearly $$\mathrm {G}_2$$ G 2 manifolds.
ISSN:0232-704X
1572-9060
DOI:10.1007/s10455-022-09853-1