Lagrangian Curves in Affine Symplectic 4-space
Emilio Musso, Evelyne Hubert (INRIA Sophia Antipolis)
TL;DR
This paper explores the geometry of Lagrangian curves in affine symplectic 4-space, establishing classifications, constructions, and geodesic characterizations within this mathematical framework.
Contribution
It introduces a natural affine symplectic frame for Lagrangian curves and classifies those with constant symplectic curvatures, also constructing Lagrangian tori and identifying geodesics.
Findings
Classification of Lagrangian curves with constant symplectic curvatures
Construction of Lagrangian tori in affine symplectic 4-space
Determination of Lagrangian geodesics
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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Taxonomy
TopicsNonlinear Waves and Solitons · Geometric and Algebraic Topology · Geometric Analysis and Curvature Flows