Collapsing of Calabi-Yau manifolds and special Lagrangian submanifolds

Yuguang Zhang

Abstrakt

In this paper, the relationship  between the existence of special Lagrangian submanifolds and the collapsing of Calabi–Yau manifolds is studied. First, special Lagrangian fibrations are constructed on some regions of bounded curvature and sufficiently collapsed in Ricci-flat Calabi–Yau manifolds. Then, conversely, it is shown that  the existence of special Lagrangian submanifolds with small volume implies the collapsing of some regions in the ambient Calabi–Yau manifolds.

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