Annals of Global Analysis and Geometry

, Volume 18, Issue 3–4, pp 405–435 | Cite as

Calibrated Embeddings in the Special Lagrangian and Coassociative Cases

  • Robert L. Bryant


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.

Calabi–Yau calibrations coassociative special Lagrangian 


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© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Robert L. Bryant
    • 1
  1. 1.Department of MathematicsDuke UniversityDurhamU.S.A.

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