A Uniqueness Theorem for Gluing Special Lagrangian Submanifolds
Yohsuke Imagi
TL;DR
This paper proves a uniqueness theorem for the gluing of flat special Lagrangian tori in a complex 3-torus, extending understanding of special Lagrangian submanifold constructions.
Contribution
It establishes a uniqueness result for the gluing of flat special Lagrangian tori, providing new insights into their geometric structure and classification.
Findings
Uniqueness of the gluing construction for flat special Lagrangian tori.
Extension of previous existence results to a uniqueness context.
Clarification of the geometric conditions under which the gluing is unique.
Abstract
Butscher, D. Lee, Y. Lee, and Joyce constructed a special Lagrangian submanifold by gluing a Lawlor neck into a transverse intersection point of two special Lagrangian submanifolds. We prove a uniqueness theorem for the gluing of flat special Lagrangian tori of real dimension 3 in a flat complex torus of complex dimension 3.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Geometric and Algebraic Topology