Mathematics#Legendre Transformation, Geometry, Differential Equations🔬 ResearchAnalyzed: Jan 3, 2026 16:18
Geometric Interpretation of Legendre Transformation
Published:Dec 28, 2025 14:13
•1 min read
•ArXiv
Analysis
This paper provides a geometric understanding of the Legendre transformation, a fundamental concept in physics and mathematics, using the Legendrian lift. It clarifies the origin of singularities in dual curves and explores applications to the Clairaut equation and contact transformations. The focus on geometric intuition makes the topic more accessible.
Key Takeaways
- •Presents a geometric interpretation of the Legendre transformation using the Legendrian lift.
- •Explains the appearance of singularities in dual curves.
- •Applies the Legendre transformation to the Clairaut differential equation.
- •Discusses contact transformations, including an infinite group different from the Legendre transformation.
Reference
“The paper explains the appearance of singularities of dual curves and considers applications to the Clairaut differential equation.”