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We prove new variation formulae for the volume of coassociative submanifolds,expressed in terms of $G_2$ data. As a special case, we obtain a secondvariation formula for variations within the moduli space of coassociativesubmanifolds; this formula highlights the role of the ambient torsion and Riccicurvature. These results apply, for example, to coassociative fibrations. Weillustrate our formulae with several examples, both homogeneous and non.

Variation formulae for the volume of coassociative submanifolds