Abstract
Every closed, oriented, real analytic Riemannian3–manifold can be isometrically embedded as a specialLagrangian submanifold of a Calabi–Yau 3–fold, even as thereal locus of an antiholomorphic, isometric involution. Every closed,oriented, real analytic Riemannian 4–manifold whose bundle of self-dual2–forms is trivial can be isometrically embedded as a coassociativesubmanifold in a G2-manifold, even as the fixed locus of ananti-G2 involution.
These results, when coupledwith McLean's analysis of the moduli spaces of such calibratedsubmanifolds, yield a plentiful supply of examples of compact calibratedsubmanifolds with nontrivial deformation spaces.
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Bryant, R.L. Calibrated Embeddings in the Special Lagrangian and Coassociative Cases. Annals of Global Analysis and Geometry 18, 405–435 (2000). https://doi.org/10.1023/A:1006780703789
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DOI: https://doi.org/10.1023/A:1006780703789