Lagrangian Curves in Affine Symplectic 4-space

2013/05/14 by Emilio Musso, Musso, Emilio, Évelyne Hubert +1 · 1 citation
Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Nonlinear Waves and Solitons #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1305.3092

openalex publication_date 2013/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Lagrangian curves in 4-space entertain intriguing relationships with second order deformation of plane curves under the special affine group and null curves in a 3-dimensional Lorentzian space form. We provide a natural affine symplectic frame for Lagrangian curves. It allows us to classify Lagrangrian curves with constant symplectic curvatures, to construct a class of Lagrangian tori and determine Lagrangian geodesics.

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• On the classification of Jacobi curves and their conformal curvatures

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