Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 5 (2009), 067, 18 pages      arXiv:0906.5607      https://doi.org/10.3842/SIGMA.2009.067
Contribution to the Special Issue “Élie Cartan and Differential Geometry”

Symplectic Applicability of Lagrangian Surfaces

Emilio Musso a and Lorenzo Nicolodi b
a) Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy
b) Dipartimento di Matematica, Università degli Studi di Parma, Viale G.P. Usberti 53/A, I-43100 Parma, Italy

Received February 25, 2009, in final form June 15, 2009; Published online June 30, 2009

Abstract
We develop an approach to affine symplectic invariant geometry of Lagrangian surfaces by the method of moving frames. The fundamental invariants of elliptic Lagrangian immersions in affine symplectic four-space are derived together with their integrability equations. The invariant setup is applied to discuss the question of symplectic applicability for elliptic Lagrangian immersions. Explicit examples are considered.

Key words: Lagrangian surfaces; affine symplectic geometry; moving frames; differential invariants; applicability.

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