Variation formulae for the volume of coassociative submanifolds

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Abstract: We prove new variation formulae for the volume of coassociative submanifolds, expressed in terms of

G_{2}

data. The main result concerns variations within the moduli space of coassociative submanifolds. If the submanifold is totally geodesic, its stability depends only on the ambient Ricci curvature. Our results apply, for example, to coassociative fibrations.

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