Some families of special Lagrangian tori

Details Some families of special Lagrangian tori Some families of special Lagrangian tori

2000-11-09

arxiv.org/abs/math/0011061v1

Mathematics

Differential Geometry

20 pages

Scientific paper

We give a simple proof of the local version of a result of R. Bryant, stating that any 3-dimensional Riemannian manifold can be isometrically embedded as a special Lagrangian submanifold in a Calabi-Yau manifold. We refine the theorem proving that a certain class of one-parameter families of metrics on a 3-torus can be isometrically embedded in a Calabi-Yau manifold as a one-parameter family of special Lagrangian submanifolds. We use our examples of one-parameter families to show that the semi-flat metric on the mirror manifold proposed be N. Hitchin is not necessarily Ricci-flat in dimension 3.

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