Invariants and submanifolds in almost complex geometry

TL;DR

This paper develops an algebraic framework for differential invariants in almost complex geometry, enabling classification of structures and analysis of pseudoholomorphic submanifolds.

Contribution

It introduces the algebra of differential invariants for GL(n,C)-structures and applies it to classify almost complex structures and study submanifolds.

Findings

Classification of almost complex structures in general positions

Identification of invariants relevant to pseudoholomorphic submanifolds

Framework for existence problems of higher-dimensional submanifolds

Abstract

In this paper we describe the algebra of differential invariants for GL(n,C)-structures. This leads to classification of almost complex structures of general positions. The invariants are applied to the existence problem of higher-dimensional pseudoholomorphic submanifolds.