Geodesics of positive Lagrangians in Milnor fibers

Jake P. Solomon, Amitai M. Yuval*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

The space of positive Lagrangians in an almost Calabi-Yau manifold is an open set in the space of all Lagrangian submanifolds. A Hamiltonian isotopy class of positive Lagrangians admits a natural Riemannian metric γ, which gives rise to a notion of geodesics. We study geodesics of positive On(ℝ) invariant Lagrangian spheres in n-dimensional A m Milnor fibers. We show the existence and uniqueness of smooth solutions to the initial value problem and the boundary value problem. In particular, we obtain examples of smooth geodesics of positive Lagrangians in arbitrary dimension. As an application, we show that the Riemannian metric γ induces a metric space structure on the space of positive On(ℝ) invariant Lagrangian spheres in the above-mentioned Milnor fibers.

Original languageAmerican English
Pages (from-to)830-868
Number of pages39
JournalInternational Mathematics Research Notices
Volume2017
Issue number3
DOIs
StatePublished - 1 Feb 2017

Bibliographical note

Publisher Copyright:
© The Author(s) 2016. Published by Oxford University Press.

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