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Deformations of asymptotically cylindrical coassociative submanifolds with fixed boundary. (English) Zbl 1106.53038

The authors show that the moduli space of coassociative deformations of a noncompact, asymptotically cylindrical coassociative 4-fold \(C\) in an asymptotically cylindrical \(G_2\)-manifold \(\left( M,\varphi , g\right)\) is also a smooth manifold. Its dimension is the dimension of the positive subspace of the image of \(H^2_{cs}\left( C,\mathbb{R}\right)\) in \(H^2 \left( C,\mathbb{R}\right)\).

MSC:

53C38 Calibrations and calibrated geometries
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
58J05 Elliptic equations on manifolds, general theory
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