A canonical way to deform a Lagrangian submanifold

Abstract

We derive some important geometric identities for Lagrangian submanifolds immersed in a Kähler 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.

16 pages, AMS-TeX. This replacement contains only minor changes. Corollary 2.8 was wrong and has been removed. Proposition 2.9 has been renamed into Proposition 2.8 and we also added a new theorem (Theorem 2.9). In addition the format and some of the questions and remarks have been altered. The author apologizes for any inconvenience

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• Singularities of Equivariant Lagrangian Mean Curvature Flow
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• Non-existence of eternal solutions to Lagrangian mean curvature flow with non-negative Ricci curvature
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• Remarks on mirror symmetry of Donaldson-Thomas theory for Calabi-Yau 4-folds
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• Generalized Lagrangian mean curvature flows in almost Calabi-Yau manifolds
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• $f$-minimal Lagrangian Submanifolds in Kähler Manifolds with Real Holomorphy Potentials
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• Convergence of Lagrangian mean curvature flow in Kähler-Einstein manifolds
• Gauss Maps of the Mean Curvature Flow
• Mean Curvature Flows of Lagrangian Submanifolds with Convex Potentials
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