Some classificational problems in four-dimensional geometry: distributions, almost complex structures and Monge-Ampere equations

TL;DR

This paper explores three interconnected classification problems in four-dimensional geometry, focusing on distributions, almost complex structures, and Monge-Ampère equations, providing new insights into their local and global structures.

Contribution

It offers a novel classification framework linking distributions, almost complex structures, and Monge-Ampère equations on four-dimensional manifolds.

Findings

Classification of locally regular distributions

Description of almost complex structures in terms of distributions

Classification of nondegenerate Monge-Ampère equations with two variables

Abstract

In this paper we consider three deeply connected classificational problems on four-dimensional manifolds. First we consider and describe locally regular distributions. Second we give a classification of almost complex structures of general position in terms of distributions. Finally we classify nondegenerate Monge-Ampere equations with two variables in terms of e-structures.