Geodesics of Hofer’s metric on the space of Lagrangian submanifolds |
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| Authors: | Hiroshi Iriyeh Takashi Otofuji |
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| Affiliation: | (1) School of Engineering, Tokyo Denki University, Kanda-Nishiki-Cho, Chiyoda-Ku, Tokyo 101-8457, Japan;(2) College of Engineering, Nihon University, Koriyama, Fukushima 963-8642, Japan |
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| Abstract: | We study geodesics of Hofer’s metric on the space of Lagrangian submanifolds in arbitrary symplectic manifolds from the variational point of view. We give a characterization of length–critical paths with respect to this metric. As a result, we see that if two Lagrangian submanifolds are disjoint then we cannot join them by length-minimizing geodesics. |
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| Keywords: | Primary 53D12 Secondary 53C60 Secondary 58D10 |
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