0x030 Differential Geometry

Summary of differential geometry of curves and surfaces [1]

Curves

Parametrized Curves

Definition 1.1 (parametrized curve) A parametrized curve in $mathbf{R}^n$ is a smooth function $\gamma: I \to \mathbf{R}^n$ where $I \in \mathbf{R}$ is an interval

Additional Topics in Curves

Surfaces

The curvature of a surface

Geodesics

The Gauss-Bonnet Theorem

Reference

[1] Tapp, Kristopher. Differential geometry of curves and surfaces. Springer, 2016.