Riemannian | Geometry.pdf

: Solving the second-order differential equation that describes the path of a particle in free fall:

, which represent how the coordinate system twists and turns across the manifold. Riemannian Geometry.pdf

d2xkdt2+Γijkdxidtdxjdt=0d squared x to the k-th power over d t squared end-fraction plus cap gamma sub i j end-sub to the k-th power d x to the i-th power over d t end-fraction d x to the j-th power over d t end-fraction equals 0 Riemannian Geometry.pdf

: Calculation of the symbols of the second kind, Γijkcap gamma sub i j end-sub to the k-th power Riemannian Geometry.pdf