2005•Unpublished venueRequires access

Super Calabi-Yau's and Special Lagrangians

R. Ricci

Abstract

We apply mirror symmetry to the super Calabi-Yau manifold CP^{(n|n+1)} and show that the mirror can be recast in a form which depends only on the superdimension and which is reminiscent of a generalized conifold. We discuss its geometrical properties in comparison to the familiar conifold geometry. In the second part of the paper examples of special-Lagrangian submanifolds are constructed for a class of super Calabi-Yau's. We finally comment on their infinitesimal deformations.

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Key concepts: Conifold, Calabi–Yau manifold, Mirror symmetry, Infinitesimal, Pure mathematics, Mathematics, Differential geometry, Manifold (fluid mechanics)