Collapsing of Calabi-Yau manifolds and special lagrangian submanifolds

Abstract

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, in the opposite direction,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.

A new result is obtained

References in corpus (3)

• Generalized special Lagrangian fibration for Calabi-Yau hypersurfaces in toric varieties III: The smooth fibres
• H-minimal Lagrangian fibrations in Kahler manifolds and minimal Lagrangian vanishing tori in Kahler-Einstein manifolds
• Convergence of Calabi-Yau manifolds

Cited by in corpus (3)

• Continuity of Extremal Transitions and Flops for Calabi-Yau Manifolds
• Open Gromov-Witten Invariants on Elliptic K3 Surfaces and Wall-Crossing
• The Strominger-Yau-Zaslow conjecture and its impact