Authors: Giordano Colò
Comments: 28 Pages.
We describe the deformations of the moduli space M of Special Lagrangian submanifolds in the compact case and we give a characterization of the topology of M by using McLean theorem. We consider Banach spaces on bundle sections and elliptical operators and we use Hodge theory to study the topology of the manifold. Starting from McLean results, for which the moduli space of compact special Lagrangian submanifolds is smooth and its tangent space can be identified with harmonic 1-forms on these submanifolds, we can analyze their deformations. Then we introduce a Riemannian metric on M, from which we obtain other important properties.
In this article, we highlight some properties of the Apollonius circles of rank - 1 associated with a triangle.