Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Contact structures of type $G_2$ associated to solutions of Noth's equation

Matthew Randall

Abstract

We establish a correspondence between solutions of Noth's equation, a non-linear ordinary differential equation that shows up in the theory of $(2,3,5)$-distributions, and diffeomorphisms of any contact structure of type $G_{2}$ to the standard one.

Contact structures of type $G_2$ associated to solutions of Noth's equation

Abstract

We establish a correspondence between solutions of Noth's equation, a non-linear ordinary differential equation that shows up in the theory of -distributions, and diffeomorphisms of any contact structure of type to the standard one.
Paper Structure (6 sections, 4 theorems, 75 equations, 1 figure)

This paper contains 6 sections, 4 theorems, 75 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Background material on contact structures of type $G_2$
  3. Contact structures of type $G_2$ associated to the solution $H(t)=3t^2$ of Noth's equation
  4. Contact structures of type $G_2$ associated to solutions of Noth's equation
  5. Proof of Theorem \ref{['maintheorem']}
  6. Transformation to $(2,3,5)$-distributions

Key Result

Theorem 1.1

There is a one-to-one correspondence between $SL(2,K)$-equivalent solutions of Noth's equation and isomorphisms of $S^3(V)$ with $\mathcal{C}$ with specified fibre parameter.

Figures (1)

  • Figure :

Theorems & Definitions (5)

  • Theorem 1.1
  • Theorem 4.1
  • Theorem 4.2
  • proof
  • Proposition 6.1