Calibrated Embeddings in the Special Lagrangian and Coassociative Cases |
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Authors: | Robert L Bryant |
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Institution: | (1) Department of Mathematics, Duke University, Box 90320, Durham, NC, 27708–0320, U.S.A. |
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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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Keywords: | Calabi– Yau calibrations coassociative special Lagrangian |
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