Unit · year 3
MU-306 · Differential Geometry
Threads space4 theorems
Curvature of curves and surfaces, and the theorems that make it intrinsic.
Theorems in this unit
T-105
The Frenet–Serret formulas
Curvature and torsion determine a space curve.
T-106
The first fundamental form
Lengths and angles on a surface from its metric.
T-107
Gauss's Theorema Egregium
Gaussian curvature is intrinsic to the surface.
T-108
The Gauss–Bonnet theorem
Total curvature is a topological invariant.