A canonical way to deform a Lagrangian submanifold
Knut Smoczyk (Harvard University)
TL;DR
This paper establishes fundamental geometric identities for Lagrangian submanifolds in Kähler manifolds and introduces a canonical deformation method via a parabolic flow in Ricci-flat Calabi-Yau spaces.
Contribution
It provides new geometric identities and a canonical deformation process for Lagrangian submanifolds in Ricci-flat Calabi-Yau manifolds.
Findings
Derived key geometric identities for Lagrangian submanifolds
Proved existence of a canonical deformation flow
Applicable in Ricci-flat Calabi-Yau ambient spaces
Abstract
We derive some important geometric identities for Lagrangian submanifolds immersed in a K\"ahler manifold and prove that there exists a canonical way to deform a Lagrangian submanifold by a parabolic flow through a family of Lagrangian submanifolds if the ambient space is a Ricci-flat Calabi-Yau manifold.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Geometric and Algebraic Topology