Arnold’s PDE

Tangent Planes of 1-Graphs in Contact Structure

Geometric Structure in the Space of 1-Jets

Geometric Interpretation of the Solutions of the Eikonal Equation (Arnold’s PDE)

Theory of Support Functions

Lifting to a Legendrian Curve v.s. Blowing Up at a Point

Making Sense of Tautological Fields

Arnold’s PDE: Constructing Isotropic Manifolds & the Euler Equation Example (Updated: 17/10/2025)

1-Graph of a Solution to a 1st-Order PDE

Eikonal Equation & Application of Characteristic Vector Field

Characteristic Direction Field of a First-Order Partial Differential Equation

Symplectic Structure & Characteristic Vector Field

Exterior Differentiation (Part 2)

Manifolds in the Space of 1-Jets