Mean curvature vector and symplectic topology of Lagrangian submanifolds in Einstein-Kähler manifolds

DOI10.1007/BF02572335zbMath0810.53045MaRDI QIDQ1340939

Yong-Geun Oh

Publication date: 21 December 1994

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/174664

zbMATH Keywords

cohomology classLagrangian submanifoldEinstein-Kähler manifoldsHamiltonian deformationsminimal Lagrangian submanifolds

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Global submanifolds (53C40) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15)

Related Items (12)

Hamiltonian stability of certain minimal Lagrangian submanifolds in complex projective spaces ⋮ A minimizing deformation of Legendrian submanifolds in the standard sphere ⋮ Symplectic spinors, holonomy and Maslov index ⋮ On the Gauss map of equivariant immersions in hyperbolic space ⋮ Symplectic topology of Lagrangian submanifolds of \(\mathbb{C}P^{n}\) with intermediate minimal Maslov numbers ⋮ Minimal Lagrangian tori and action-angle coordinates ⋮ Hamiltonian stability for weighted measure and generalized Lagrangian mean curvature flow ⋮ Hamiltonian actions and homogeneous Lagrangian submanifolds ⋮ Second variation and Legendrian stabilities of minimal Legendrian submanifolds in Sasakian manifolds ⋮ Spin\(^{c}\) geometry of Kähler manifolds and the Hodge Laplacian on minimal Lagrangian sub\-manifolds ⋮ On Lagrangian submanifolds in complex hyperquadrics and isoparametric hypersurfaces in spheres ⋮ Cyclic Lagrangian submanifolds and Lagrangian fibrations

Cites Work

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• Connections of Berry and Hannay type for moving Lagrangian submanifolds
• Calibrated geometries
• Volume minimization of Lagrangian submanifolds under Hamiltonian deformations
• Second variation and stabilities of minimal Lagrangian submanifolds in Kähler manifolds
• Sur la géométrie des sous-fibrés et des feuilletages lagrangiens

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