The branched deformations of the special Lagrangian submanifolds

2022/02/24 by Siqi He, He, Siqi · 3 citations
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2202.12282

Abstract

The branched deformations of immersed compact special Lagrangian submanifolds are studied in this paper. If there exists a nondegenerate ℤ₂ harmonic 1-form over a special Lagrangian submanifold L, we construct a family of immersed special Lagrangian submanifolds L_t, that are diffeomorphic to a branched covering of L and L_t convergence to 2L as current. This answers a question suggested by Donaldson. Combining with the work of Abouzaid and Imagi, we obtain constraints for the existence of nondegenerate ℤ₂ harmonic 1-forms.

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