Jet Spaces & Intrinsic Geometry | Differential Equations #6
Автор: jetbundle
Загружено: 2026-01-09
Просмотров: 215
Описание:
We realize that "derivatives" are not actions but independent coordinates. A differential equation is not a problem to be solved but a submanifold sitting inside a larger space called a jet bundle. Solving the equation means finding a surface that fits inside this submanifold while remaining tangent to a special "contact structure." This geometric viewpoint allows us to handle overdetermined systems, classify singularities via algebra (Spencer Cohomology), and study equations that evolve the geometry of the universe itself (Ricci Flow).
00:00 Intro
02:28 Contact Geometry
11:06 Cartan-Kahler Theorem
17:19 Gauge Theory
20:29 Self-Duality
23:48 Monge-Ampere
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