Symplectic Applicability of Lagrangian Surfaces

TL;DR

This paper develops a method using moving frames to analyze the affine symplectic geometry of Lagrangian surfaces, deriving invariants and integrability conditions, and explores symplectic applicability with explicit examples.

Contribution

It introduces a new invariant framework for elliptic Lagrangian immersions in affine symplectic space, including integrability equations and applicability criteria.

Findings

Derived fundamental invariants of elliptic Lagrangian immersions

Established integrability equations for these invariants

Provided explicit examples illustrating symplectic applicability

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.