Calibrated embeddings in the special Lagrangian and coassociative cases

Journal Article

Every closed, oriented, real analytic Riemannian 3-manifold can be isometrically embedded as a special Lagrangian submanifold of a Calabi-Yau 3-fold, even as the real locus of an antiholomorphic, isometric involution. Every closed, oriented, real analytic Riemannian 4-manifold whose bundle of self-dual 2-forms is trivial can be isometrically embedded as a coassociative submanifold in a G_2-manifold, even as the fixed locus of an anti-G_2 involution. These results, when coupled with McLean's analysis of the moduli spaces of such calibrated submanifolds, yield a plentiful supply of examples of compact calibrated submanifolds with nontrivial deformation spaces.

Full Text

Duke Authors

Cited Authors

  • Bryant, RL

Published Date

  • 2000

Published In

  • Annals of Global Analysis and Geometry

Volume / Issue

  • 18 / 3-4

Start / End Page

  • 405 - 435