Deformations of compact coassociative 4-folds with boundary

JOURNAL OF GEOMETRY AND PHYSICS

卷:59

Article

Kovalev, Alexei¹  Lotay, Jason D.² 

[1] Univ Cambridge, Ctr Mat Sci, Dept Pure Math & Math Stat, Cambridge CB3 0WB, England

[2] Math Sci Res Inst, Berkeley, CA 94720 USA

关键词: Calibrated geometries;    G(2)-manifolds;    Coassociative submanifolds;    Boundary value problems;   

DOI  :  10.1016/j.geomphys.2008.09.002

来源: Elsevier

【 摘 要 】

Let M be a 7-manifold with a G(2)-structure induced by a closed 'positive' differential 3-form. We study deformations of a compact coassociative 4-submanifold N subset of M with non-empty boundary partial derivative N contained in a fixed, codimension 1 submanifold S of M with a compatible Hermitian symplectic structure. We show that 'small' coassociative deformations of N with special Lagrangian boundary in S form a smooth moduli space of finite dimension not greater than the Betti number b(1) (partial derivative N). It is also shown that N is 'stable' under small deformations of the closed G(2) 3-form on the ambient 7-manifold M. The results can be compared to those for minimal Lagrangian submanifolds of Calabi-Yau manifolds proved in [A. Butscher, Deformations of minimal Lagrangian submanifolds with boundary, Proc. Amer. Math. Soc. 131 (2002), 1953-1964]. Some examples are also discussed. (C) 2008 Elsevier B.V. All rights reserved.

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