Geodesics of Hofer's metric on the space of Lagrangian submanifolds

DOI10.1007/s00229-007-0076-4zbMath1127.53068arXivmath/0608082OpenAlexW1970750887MaRDI QIDQ2457906

Takashi Otofuji, Hiroshi Iriyeh

Publication date: 23 October 2007

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0608082

zbMATH Keywords

geodesicssymplectic manifoldsLagrangian submanifoldsHofer geometryexact variation.length-critical paths

Mathematics Subject Classification ID

Spaces of embeddings and immersions (58D10) Lagrangian submanifolds; Maslov index (53D12) Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60)

Cites Work

• Geometry on the group of Hamiltonian diffeomorphisms
• Geodesics of Hofer's metric on the group of Hamiltonian diffeomorphisms
• Action spectrum and Hofer's distance between Lagrangian submanifolds.
• Invariant Finsler metrics on the space of Lagrangian embeddings
• The geometry of symplectic energy
• Hofer's \(L^ \infty\)-geometry: Energy and stability of Hamiltonian flows. I
• Hofer's \(L^ \infty\)-geometry: Energy and stability of Hamiltonian flows. II
• Conjugate points on geodesics of Hofer's metric
• Lagrangian intersections, symplectic energy, and areas of holomorphic curves
• Geodesics on the space of Lagrangian submanifolds in cotangent bundles
• On the topological properties of symplectic maps
• A COMPARISON OF HOFER'S METRICS ON HAMILTONIAN DIFFEOMORPHISMS AND LAGRANGIAN SUBMANIFOLDS
• Loops of Lagrangian submanifolds and pseudoholomorphic discs

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