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

Hiroshi Iriyeh·Takashi Otofuji
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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 prove that if two Lagrangian submanifolds are disjoint then we cannot join them by length-minimizing geodesics.

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Hiroshi Iriyeh, Takashi Otofuji. 2006-08-03. Geodesics of Hofer's metric on the space of Lagrangian submanifolds. https://arxiv.org/abs/math/0608082

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