Reducing almost Lagrangian structures and almost CR geometries to partially integrable structures

TL;DR

This paper introduces a method to analyze almost CR and Lagrangian geometries by associating them with uniquely defined partially integrable structures, enabling equivalence classification through isomorphisms and CR morphisms.

Contribution

It provides a novel approach to reduce almost CR and Lagrangian structures to partially integrable structures for easier analysis and classification.

Findings

Equivalent almost CR geometries generate isomorphic partially integrable structures.

CR morphisms correspond to structure-preserving maps between these geometries.

The method unifies the analysis of almost CR and Lagrangian geometries through partial integrability.

Abstract

This paper demostrates a method for analysing almost CR geometries $(H,J)$, by uniquley defining a partially integrable structure $(H,K)$ from the same data. Thus two almost CR geometries $(H,J)$ and $(H',J')$ are equivalent if and and only if they generate isomorphic induced partially integrable CR geometries $(H,K)$ and $(H',K')$, and if the set of CR morphisms between these spaces contains an element that maps $J$ to $J'$. Similar results hold for almost Lagrangian structures.