#differential-geometry

53. Differential Geometry

This volume studies smooth geometric structures using calculus. It develops curves, surfaces, manifolds, and curvature, forming the foundation for modern geometry and physics. Part I. Curves and Surfaces Chapter 1. Curves in Euclidean Space 1.1 Parametrized curves 1.2 Arc length 1.3 Curvature and torsion 1.4 Frenet frame 1.5 Examples Chapter 2. Surfaces 2.1 Parametrized surfaces 2.2 Tangent planes 2.3 First fundamental form 2.4 Surface area 2.5 Examples Chapter 3. Curvature...