Tags
Surfaces
Nov 5, 2021
Differential Geometry
64 min readDifferential Geometry (3): The Shape Operator — Curvature of Surfaces
The Gauss map and shape operator capture how a surface bends in space — principal, Gaussian, and mean curvatures classify every point as elliptic, hyperbolic, or parabolic.
Nov 3, 2021
Differential Geometry
66 min readDifferential Geometry (2): Surfaces and the First Fundamental Form: Intrinsic Measurements
Regular surfaces, coordinate patches, the tangent plane, and the first fundamental form — how to measure lengths, angles, and areas on a surface without leaving it.