1999/11/13 by Edward Goldstein, Édward Goldstein, Goldstein, Edward
Engineering · Mathematics · #53XX #Advanced Measurement and Metrology Techniques #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #math.AG #math.DG #msc:53XX
paper · pdf · doi:10.48550/arxiv.math/9911093
28 pages
openalex publication_date 1999/11/13 · arxiv created 2000/08/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we investigate the geometry of Calibrated submanifolds and study relations between their moduli-space and geometry of the ambient manifold. In particular for a Calabi-Yau manifold we define Special Lagrangian submanifolds for any Kahler metric on it. We show that for a choice of Kahler metric the Borcea-Voisin threefold has a fibration structure with generic fiber being a Special Lagrangian torus. Moreover we construct a mirror to this fibration. Also for any closed G2 form on a 7-manifold we study coassociative submanifolds and we show that one example of a G2 manifold constructed by Joyce in [10] is a fibration with generic fiber being a coassociative 4-torus. Similarly we construct a mirror to this fibration.