Geodesics on the space of Lagrangian submanifolds in cotangent bundles
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- by Darko Milinković PDF
- Proc. Amer. Math. Soc. 129 (2001), 1843-1851 Request permission
Abstract:
We prove that the space of Hamiltonian deformations of zero section in a cotangent bundle of a compact manifold is locally flat in the Hofer metric and we describe its geodesics.References
- Misha Bialy and Leonid Polterovich, Geodesics of Hofer’s metric on the group of Hamiltonian diffeomorphisms, Duke Math. J. 76 (1994), no. 1, 273–292. MR 1301192, DOI 10.1215/S0012-7094-94-07609-6
- Yu. V. Chekanov, Lagrangian intersections, symplectic energy, and areas of holomorphic curves, Duke Math. J. 95 (1998), no. 1, 213–226. MR 1646550, DOI 10.1215/S0012-7094-98-09506-0
- Andreas Floer, Cuplength estimates on Lagrangian intersections, Comm. Pure Appl. Math. 42 (1989), no. 4, 335–356. MR 990135, DOI 10.1002/cpa.3160420402
- Helmut Hofer and Eduard Zehnder, Symplectic invariants and Hamiltonian dynamics, Birkhäuser Advanced Texts: Basler Lehrbücher. [Birkhäuser Advanced Texts: Basel Textbooks], Birkhäuser Verlag, Basel, 1994. MR 1306732, DOI 10.1007/978-3-0348-8540-9
- Hermann Kober, Transformationen von algebraischem Typ, Ann. of Math. (2) 40 (1939), 549–559 (German). MR 96, DOI 10.2307/1968939
- Darko Milinković, Morse homology for generating functions of Lagrangian submanifolds, Trans. Amer. Math. Soc. 351 (1999), no. 10, 3953–3974. MR 1475690, DOI 10.1090/S0002-9947-99-02217-5
- Milinković, D., On equivalence of two constructions of invariants of Lagrangian submanifolds, Pacific J. Math., to appear.
- Yong-Geun Oh, Symplectic topology as the geometry of action functional. I. Relative Floer theory on the cotangent bundle, J. Differential Geom. 46 (1997), no. 3, 499–577. MR 1484890
- Yong-Geun Oh, Relative Floer and quantum cohomology and the symplectic topology of Lagrangian submanifolds, Contact and symplectic geometry (Cambridge, 1994) Publ. Newton Inst., vol. 8, Cambridge Univ. Press, Cambridge, 1996, pp. 201–267. MR 1432465
- Claude Viterbo, Symplectic topology as the geometry of generating functions, Math. Ann. 292 (1992), no. 4, 685–710. MR 1157321, DOI 10.1007/BF01444643
Additional Information
- Darko Milinković
- Affiliation: Department of Mathematics, University of California, Irvine, California 92697-3875
- Address at time of publication: Matematički Fakultet, Studentski trg 16, 11000 Belgrade, Serbia, Yugoslavia
- Email: dmilinko@math.uci.edu, milinko@matf.bg.ac.yu
- Received by editor(s): September 21, 1999
- Published electronically: November 3, 2000
- Communicated by: Jozef Dodziuk
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 1843-1851
- MSC (1991): Primary 58E05; Secondary 57R57, 58F05
- DOI: https://doi.org/10.1090/S0002-9939-00-05851-2
- MathSciNet review: 1814118