# Homogeneous G-structures

## TL;DR

This paper introduces homogeneous G-structures, a new framework that unifies various geometric structures including contact geometry, which traditionally does not fit into the G-structure theory.

## Contribution

The paper proposes the concept of homogeneous G-structures, extending the G-structure framework to include contact structures and other examples.

## Key findings

- Homogeneous G-structures encompass contact geometry.
- The new framework unifies multiple geometric structures.
- Examples illustrating the applicability of homogeneous G-structures.

## Abstract

The theory of $G$-structures provides us with a unified framework for a large class of geometric structures, including symplectic, complex and Riemannian structures, as well as foliations and many others. Surprisingly, contact geometry - the "odd-dimensional counterpart" of symplectic geometry - does not fit naturally into this picture. In this paper, we introduce the notion of a homogeneous $G$-structure, which encompasses contact structures, as well as some other interesting examples that appear in the literature.