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

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 $(H^{\prime },J^{\prime })$ are equivalent if and and only if they generate isomorphic induced partially integrable CR geometries $(H,K)$ and $(H^{\prime },K^{\prime })$, and if the set of CR morphisms between these spaces contains an element that maps $J$ to $J^{\prime }$. Similar results hold for almost Lagrangian structures.

6 pages, acknowledgements added