Calibrated embeddings in the special Lagrangian and coassociative cases

Details Calibrated embeddings in the special Lagrangian and coassociative cases Calibrated embeddings in the special Lagrangian and coassociative cases

1999-12-31

arxiv.org/abs/math/9912246v2

Annals of Global Analysis and Geometry 18 (2000), pp. 405-435.

Mathematics

Differential Geometry

AMS-TeX v. 2.1, 26 pages, uses amsppt.sty (2.1h), minor typos corrected

Scientific paper

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.

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