Differential Geometry

Riemannian Geometry

Riemannian geometry equips manifolds with a metric measuring length and angle, and studies their curvature. Through geodesics and the curvature tensor, it handles the geometry of curved spaces.

1 Riemannian Metric The Riemannian metric as a positive-definite symmetric 2-tensor on the tangent bundle 2022-12-16 2 Connection Differentiation on a vector bundle 2022-12-16